# questions

title: â« 0 Ï /2 â 2 s i n x + 2 c o s x 2 s i n x â d x equals
slug: 0-2-2-s-i-n-x-2-c-o-s-x-2-s-i-n-x-d-x-equals-55983
tags: ['Mathematics', 'Definite Integration', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch0.db
question:
<div class="question">$\int_{0}^{\pi / 2} \frac{2^{\sin x}}{2^{\sin x}+2^{\cos x}} d x$ equals</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\pi$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\pi / 4$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\pi / 2$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\pi / 4$</span> </div>

answer:
<div class="solution">$\mathrm{I}=\int_{0}^{\pi / 2} \frac{2^{\sin \mathrm{x}}}{2^{\sin x}+2^{\cos \mathrm{x}} \mathrm{dx}}$
<br/>$\mathrm{I}=\int_{0}^{\pi / 2} \frac{2^{\sin (\pi / 2-\mathrm{x})}}{2^{\sin (\pi / 2-\mathrm{x})}+2^{\cos (\pi / 2-\mathrm{x})} \mathrm{dx}}$
<br/>$=\int \frac{2^{\cos \mathrm{x}}}{2^{\cos \mathrm{x}}+2^{\sin \mathrm{x}}} \mathrm{dx} \Rightarrow 21=\int_{0}^{\pi / 2} \mathrm{~d} \mathrm{x}=\frac{\pi}{2} \Rightarrow 1=\frac{\pi}{4}$</div>


title: â« 0 Ï /4 â cos x e s i n x d x is equal to
slug: 0-4-cos-x-e-s-i-n-x-d-x-is-equal-to-11535
question: <div class="question">$\int_0^{\pi / 4} \cos x e^{\sin x} d x$ is equal to</div>
tags: ['Mathematics', 'Definite Integration', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$e-1$</span> </div>
source_db: MarksBatch0.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$e+1$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$e-1$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$e$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-e$</span> </li> </ul>

answer:
<div class="solution">Suppose, $I=\int_0^{\pi / 2} \cos x e^{\sin x} d x$<br/>Let $\sin x=t \Rightarrow \cos x d x=d t$<br/>$x \rightarrow 0 \Rightarrow t \rightarrow 0$<br/>and $x \rightarrow \frac{\pi}{2} \Rightarrow t \rightarrow 1$<br/>So $I=\int_0^1 e^t d t=\left[e^t\right]_0^1=e-1$</div>


tags: ['Chemistry', 'Electrochemistry', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch0.db
title:
0 . 5 F of electricity is passed through 500 mL of copper sulphate solution. The amount of copper which can be deposited will be

slug:
0-5-f-of-electricity-is-passed-through-500-ml-of-copper-sulphate-solution-the-amount-of-copper-wh-17021

question:
<div class="question"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>5</mn><mi mathvariant="normal">F</mi></math> of electricity is passed through <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mo> </mo><mi>mL</mi></math> of copper sulphate solution. The amount of copper which can be deposited will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>63</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">g</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>31</mn><mo>.</mo><mn>75</mn><mo> </mo><mi mathvariant="normal">g</mi></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>.</mo><mn>80</mn><mo> </mo><mi mathvariant="normal">g</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">unpredictable</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>.</mo><mn>80</mn><mo> </mo><mi mathvariant="normal">g</mi></math></span> </div>

answer:
<div class="solution"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>Cu</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mo>+</mo><mn>2</mn><msup><mi mathvariant="normal">e</mi><mo>-</mo></msup><mo>⟶</mo><mi>Cu</mi></math>   <math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mi mathvariant="normal">i</mi></mfenced></math></p><p>According to Faraday's first law, when an electric current is passed through an electrolyte, amount of substance deposited is directly proportional to the quantity of electric charge passed through the electrolyte.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∵</mo><mn>1</mn><mo> </mo><mi>mol</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>63</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Cu</mi></math> is obtained by passing <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi mathvariant="normal">F</mi></math> of electricity.</p><p>Mass of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Cu</mi></math> obtained by passing <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mi mathvariant="normal">F</mi></math> of electricity <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>63</mn><mo>.</mo><mn>5</mn></mrow><mn>2</mn></mfrac><mi mathvariant="normal">g</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Mass of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Cu</mi></math> obtained by passing <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>5</mn><mi mathvariant="normal">F</mi></math> of electricity<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>63</mn><mo>.</mo><mn>5</mn></mrow><mn>2</mn></mfrac><mo>×</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>=</mo><mn>15</mn><mo>.</mo><mn>80</mn><mo> </mo><mi mathvariant="normal">g</mi></math></p></div>


title: â« 0 10 â ( 10 â x ) 10 + x 10 x 10 â d x is equal to
slug: 0-10-10-x-10-x-10-x-10-d-x-is-equal-to-21018
question: <div class="question">$\int_{0}^{10} \frac{x^{10}}{(10-x)^{10}+x^{10}} d x$ is equal to</div>
tags: ['Mathematics', 'Definite Integration', 'BITSAT', 'BITSAT 2014']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch0.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">10</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">5</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{0}$</span> </li> </ul>

answer:
<div class="solution">Let $I=\int_{0}^{10} \frac{x^{10}}{(10-x)^{10}+x^{10}} d x$...(1)
<br/> <br/>$I=\int_{0}^{10} \frac{(10-x)^{10}}{(10-x)^{10}+x^{10}} d x$...(2)
<br/> <br/>Adding
<br/> <br/>(1) and (2), we get
<br/> <br/>$2 I=\int_{0}^{10} d x \Rightarrow 2 I=10 \Rightarrow I=5$</div>


tags: ['Chemistry', 'Redox Reactions', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch0.db
title:
0 . 45 g acid of molecular mass 90 was neutralise by 20 ml of 0 . 5 N KOH . The basicity of the acid is

slug:
0-45-g-acid-of-molecular-mass-90-was-neutralise-by-20-ml-of-0-5-n-koh-the-basicity-of-the-acid-76403

question:
<div class="question"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>45</mn><mo> </mo><mi mathvariant="normal">g</mi></math> acid of molecular mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn></math> was neutralise by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ml</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">N</mi><mo> </mo><mi>KOH</mi></math>. The basicity of the acid is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></span> </div>

answer:
<div class="solution"><p>Given that <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>45</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of the acid of molecular mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn></math> was neutralized by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mi>ml</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>5</mn><mo> </mo><mfenced><mi mathvariant="normal">N</mi></mfenced></math> caustic potash.</p><p>We know that,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Normality</mi><mo> </mo><mfenced><mi mathvariant="normal">N</mi></mfenced><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mi>Weight</mi><mo> </mo><mi>of</mi><mo> </mo><mi>the</mi><mo> </mo><mi>base</mi><mo> </mo><mo>×</mo><mn>1000</mn></mrow><mrow><mi>Eq</mi><mo>.</mo><mo> </mo><mi>weight</mi><mo>×</mo><mi>volume</mi></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∵</mo></math> Gram equivalents of an acid</p><p>Gram equivalents of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>KOH</mi></math> i.e. <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>0</mn><mo>.</mo><mn>45</mn></mrow><mi mathvariant="normal">E</mi></mfrac><mo>=</mo><mfrac><mrow><mn>20</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow><mn>1000</mn></mfrac></math></p><p>where, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">E</mi><mo>=</mo></math> Equivalent mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">E</mi><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>45</mn><mo>×</mo><mn>1000</mn></mrow><mrow><mn>20</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfrac><mo>=</mo><mn>45</mn></math></p><p>Thus, basicity <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>90</mn><mn>45</mn></mfrac><mo>=</mo><mn>2</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>∵</mo><mi>Basicity</mi><mo>=</mo><mfrac><mrow><mi>Molecular</mi><mo>mass</mo></mrow><mrow><mi>Equivalent</mi><mo>mass</mo></mrow></mfrac></mrow></mfenced></math></p></div>


slug: 0-765-g-of-an-acid-gives-0-535-g-of-co-2-and-0-138-g-of-h-2-o-then-the-ratio-of-percentage-40062
tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch0.db
title:
0 . 765 g of an acid gives 0 . 535 g of CO 2 and 0 . 138 g of H 2 O . Then, the ratio of percentage of carbon and hydrogen is

question:
<div class="question"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>765</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of an acid gives <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>535</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CO</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>138</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi></math>. Then, the ratio of percentage of carbon and hydrogen is </div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19</mn><mo>:</mo><mn>2</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>:</mo><mn>17</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo>:</mo><mn>17</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>:</mo><mn>7</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19</mn><mo>:</mo><mn>2</mn></math></span> </div>

answer:
<div class="solution"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>%</mo></math> for <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CO</mi><mn>2</mn></msub></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∵</mo><mo> </mo><mn>0</mn><mo>.</mo><mn>765</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of acid gives <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CO</mi><mn>2</mn></msub><mo>=</mo><mn>0</mn><mo>.</mo><mn>535</mn><mo> </mo><mi mathvariant="normal">g</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mn>100</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of acid gives <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CO</mi><mn>2</mn></msub><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>535</mn><mo>×</mo><mn>100</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>765</mn></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>%</mo></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CO</mi><mn>2</mn></msub><mo>=</mo><mn>70</mn><mo>.</mo><mn>00</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>%</mo></math> for carbon </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∵</mo><mo> </mo><mn>44</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CO</mi><mn>2</mn></msub></math> gives, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">C</mi><mo>=</mo><mn>12</mn><mo> </mo><mi mathvariant="normal">g</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mn>70</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CO</mi><mn>2</mn></msub></math> gives, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">C</mi><mo>=</mo><mfrac><mrow><mn>12</mn><mo>×</mo><mn>70</mn></mrow><mn>44</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>19</mn><mo>.</mo><mn>09</mn><mo> </mo><mi mathvariant="normal">g</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mo>%</mo></math> of carbon <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>19</mn><mo>.</mo><mn>00</mn></math></p><p>Similarly, </p><p>(i) for hydrogen </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>%</mo></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>138</mn><mo>×</mo><mn>100</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>765</mn></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>18</mn><mo>.</mo><mn>03</mn><mo>=</mo><mn>18</mn><mo>.</mo><mn>00</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>%</mo></math> of Hydrogen</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mfrac><mrow><mn>2</mn><mo>×</mo><mn>18</mn></mrow><mn>18</mn></mfrac><mo>=</mo><mn>2</mn><mo>.</mo><mn>00</mn></math></p><p>Hence ratio of carbon and hydrogen is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19</mn><mo>:</mo><mn>2</mn></math></p></div>


title: â« 0 â â ( x 2 + a 2 ) ( x 2 + b 2 ) dx â is
slug: 0-x-2-a-2-x-2-b-2-dx-is-73205
tags: ['Mathematics', 'Definite Integration', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch0.db
question:
<div class="question">$\int_{0}^{\infty} \frac{\mathrm{dx}}{\left(\mathrm{x}^{2}+\mathrm{a}^{2}\right)\left(\mathrm{x}^{2}+\mathrm{b}^{2}\right)}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\pi a b}{a+b}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\pi}{2(a+b)}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{\pi}{2 a b(a+b)}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\pi(a+b)}{2 a b}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\pi}{2 a b(a+b)}$</span> </div>

answer:
<div class="solution">$\int_{0}^{\infty} \frac{d x}{\left(x^{2}+a^{2}\right)\left(x^{2}+b^{2}\right)}=\frac{1}{b^{2}-a^{2}}$
<br/> <br/>$\int_{0}^{\infty} \frac{\left(x^{2}+b^{2}\right)-\left(x^{2}+a^{2}\right)}{\left(x^{2}+a^{2}\right)\left(x^{2}+b^{2}\right)}$
<br/> <br/>$=\frac{1}{b^{2}-a^{2}} \int_{0}^{\infty}\left[\frac{1}{x^{2}+a^{2}}-\frac{1}{x^{2}+b^{2}}\right] d x$
<br/> <br/>$=\frac{1}{b^{2}-a^{2}}\left[\frac{1}{a} \tan ^{-1} \frac{x}{a}-\frac{1}{b} \tan ^{-1} \frac{x}{b}\right]_{0}^{\infty}$
<br/> <br/>$=\frac{1}{b^{2}-a^{2}}\left[\frac{\pi}{2 a}-\frac{\pi}{2 b}\right]=\frac{\pi}{2 a b(a+b)}$</div>


title: 2 3 n â 7 n â 1 is divisible by
slug: 2-3-n-7-n-1-is-divisible-by-22153
question: <div class="question">$2^{3 n}-7 n-1$ is divisible by</div>
tags: ['Mathematics', 'Basic of Mathematics', 'BITSAT', 'BITSAT 2014']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">49</span> </div>
source_db: MarksBatch0.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">64</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">36</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">49</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">25</span> </li> </ul>

answer:
<div class="solution">$2^{3 n}-7 n-1 \quad$ Taking $n=2 ;$
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>2^{6}-7 \times 2-1 \\
<br/> <br/>=64-15=49
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>Therefore this is divisible by 49 .</div>


slug: 2-n-2-o-5-4-no-2-o-2-if-rate-and-rate-constant-for-above-reaction-are-2-40-28649
tags: ['Chemistry', 'Chemical Kinetics', 'BITSAT', 'BITSAT 2012']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0.8</span> </div>
source_db: MarksBatch0.db
title:
2 N 2 â O 5 â â 4 NO 2 â + O 2 â If rate and rate constant for above reaction are 2.40 Ã 1 0 â 5 mol L â 1 s â 1 and 3 Ã 1 0 â 5 s â 1 respectively, then calculate the concentration of N 2 â O 5 â

question:
<div class="question">$2 \mathrm{~N}_{2} \mathrm{O}_{5} \rightleftharpoons 4 \mathrm{NO}_{2}+\mathrm{O}_{2}$
<br/>If rate and rate constant for above reaction are $2.40 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$ and $3 \times 10^{-5} \mathrm{~s}^{-1}$ respectively, then calculate the concentration of $\mathrm{N}_{2} \mathrm{O}_{5}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1.4</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">1.2</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">0.04</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">0.8</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">The reaction is of first and for a first order reaction, rate, $R=k\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right]$ $2.4 \times 10^{-5}=3 \times 10^{-5} \times\left[\mathrm{N}_{2} \mathrm{O}_{5}\right]$
<br/>$\left[\mathrm{N}_{2} \mathrm{O}_{5}\right]=\frac{2.4 \times 10^{-5}}{3 \times 10^{-5}}=0.8 \mathrm{~mol} \mathrm{~L}^{-1}$</div>


title: â« Ï /3 Ï /2 â x sin ( Ï [ x ] â x ) dx is equal to
slug: 3-2-x-sin-x-x-dx-is-equal-to-52084
question: <div class="question">$\int_{\pi / 3}^{\pi / 2} x \sin (\pi[x]-x) \mathrm{dx}$ is equal to</div>
tags: ['Mathematics', 'Definite Integration', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch0.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{2}+\frac{\pi}{6}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$1-\frac{\sqrt{3}}{2}+\frac{\pi}{6}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$-\frac{1}{2}-\frac{\pi}{6}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\sqrt{3}}{2}-1-\frac{\pi}{6}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1-\frac{\sqrt{3}}{2}+\frac{\pi}{6}$</span> </div>

answer:
<div class="solution">In the interval $\frac{\pi}{3}$ to $\frac{\pi}{2},[\mathrm{x}]=1$ $\begin{aligned} \therefore \mathrm{I} &amp;=\int_{\pi / 3}^{\pi / 2} \mathrm{x} \sin (\pi-\mathrm{x}) \mathrm{dx}=\int_{\pi / 3}^{\pi / 2} \mathrm{x} \sin \mathrm{x} \mathrm{d} \mathrm{x} \\ &amp;=[-\mathrm{x} \cos \mathrm{x}+\sin \mathrm{x}]_{\pi / 3}^{\pi / 2}=1-\frac{\sqrt{3}}{2}+\frac{\pi}{6} \end{aligned}$</div>


tags: ['Physics', 'Kinetic Theory of Gases', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch0.db
title:
3 moles of an ideal gas at a temperature of 2 7 â C are mixed with 2 moles of an ideal gas at a temperature 22 7 â C , determine the equilibrium temperature of the mixture, assuming no loss of energy.

slug:
3-moles-of-an-ideal-gas-at-a-temperature-of-2-7-c-are-mixed-with-2-moles-of-an-ideal-gas-at-a-te-38040

question:
<div class="question">3 moles of an ideal gas at a temperature of $27^{\circ} \mathrm{C}$ are mixed with 2 moles of an ideal gas at a temperature $227^{\circ} \mathrm{C}$, determine the equilibrium temperature of the mixture, assuming no loss of energy.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$327^{\circ} \mathrm{C}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$107^{\circ} \mathrm{C}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$318^{\circ} \mathrm{C}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$410^{\circ} \mathrm{C}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$107^{\circ} \mathrm{C}$</span> </div>

answer:
<div class="solution">Energy possessed by the ideal gas at $27^{\circ} \mathrm{C}$ is<br/>$$<br/>E_{1}=3\left(\frac{3}{2} R \times 300\right)=\frac{2700 R}{2}<br/>$$<br/>Energy possessed by the ideal gas at $227^{\circ} \mathrm{C}$ is<br/>$$<br/>\mathrm{E}_{2}=2\left(\frac{3 \mathrm{R}}{2} \times 500\right)=1500 \mathrm{R}<br/>$$<br/>If $\mathrm{T}$ be the equilibrium temperature, of the mixture, then its energy will be<br/>$$<br/>\mathrm{E}_{\mathrm{m}}=5\left(\frac{3 \mathrm{R} \mathrm{T}}{2}\right)<br/>$$<br/>Since, energy remains conserved,<br/>$$<br/>\mathrm{E}_{\mathrm{m}}=\mathrm{E}_{1}+\mathrm{E}_{2}<br/>$$<br/>or $\quad 5\left(\frac{3 R T}{2}\right)=\frac{2700 R}{2}+1500 R$<br/>or $\quad \mathrm{T}=380 \mathrm{~K}$ or $107^{\circ} \mathrm{C}$</div>


tags: ['Chemistry', 'Redox Reactions', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch0.db
title:
4 g of copper was dissolved in conc . HNO 3 . The copper nitrate thus obtained gave 5 g of its oxide on strong heating the equivalent weight of copper is

slug:
4-g-of-copper-was-dissolved-in-conc-hno-3-the-copper-nitrate-thus-obtained-gave-5-g-of-its-oxide-46684

question:
<div class="question"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of copper was dissolved in <math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mi>conc</mi><mo>.</mo><msub><mi>HNO</mi><mn>3</mn></msub></math>. The copper nitrate thus obtained gave <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of its oxide on strong heating the equivalent weight of copper is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>23</mn></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>32</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>32</mn></math></span> </div>

answer:
<div class="solution"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of copper gave <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of its oxide means,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of oxygen combine with <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of copper.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∵</mo></math> Eq. wt of oxygen <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>8</mn></math>,</p><p>Therefore, </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of oxygen combine with <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>4</mn><mo>×</mo><mn>8</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of copper <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>32</mn><mo> </mo><mi mathvariant="normal">g</mi></math></p><p>Hence, </p><p>Equivalent weight of copper <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>32</mn></math></p></div>


slug: 4-moles-of-a-are-mixed-with-4-moles-of-b-at-equilibrium-for-the-reaction-a-b-c-d-2-moles-32528
tags: ['Chemistry', 'Chemical Equilibrium', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch0.db
title:
4 moles of A are mixed with 4 moles of B . At equilibrium for the reaction A + B â C + D , 2 moles of C and D are formed, the equilibrium constant for the reaction will be,

question:
<div class="question"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> moles of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi></math> are mixed with <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> moles of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">B</mi></math>. At equilibrium for the reaction <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi><mo>+</mo><mi mathvariant="normal">B</mi><mo>⇌</mo><mi mathvariant="normal">C</mi><mo>+</mo><mi mathvariant="normal">D</mi><mo>,</mo><mo> </mo><mn>2</mn></math> moles of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">C</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">D</mi></math> are formed, the equilibrium constant for the reaction will be,</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>/</mo><mn>2</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>/</mo><mn>4</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span> </div>

answer:
<div class="solution"><p>The initial concentrations of A, B, C, and D are 4M, 4M, 0M, and 0M respectively.</p><p>The equilibrium concentrations of A,B,C and D are 4−2=2M, 4−2=2M, 2M and 2M respectively.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mi mathvariant="normal">A</mi><mo> </mo><mo> </mo><mo> </mo><mo>+</mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mi mathvariant="normal">B</mi><mo> </mo><mo> </mo><mo>⇌</mo><mo> </mo><mo> </mo><mi mathvariant="normal">C</mi><mo> </mo><mo> </mo><mo> </mo><mo>+</mo><mo> </mo><mo> </mo><mo> </mo><mi mathvariant="normal">D</mi><mspace linebreak="newline"></mspace><mi>initial</mi><mo> </mo><mi>conc</mi><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mn>4</mn><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mn>4</mn><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mn>0</mn><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mn>0</mn><mspace linebreak="newline"></mspace><mi>at</mi><mo> </mo><mi>equilibrium</mi><mo> </mo><mfenced><mrow><mn>4</mn><mo>-</mo><mn>2</mn></mrow></mfenced><mo> </mo><mo> </mo><mo> </mo><mfenced><mrow><mn>4</mn><mo>-</mo><mn>2</mn></mrow></mfenced><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mn>2</mn><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mn>2</mn></math></p><p>The expression for the equilibrium constant is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mo>[</mo><mi mathvariant="normal">C</mi><mo>]</mo><mo>[</mo><mi mathvariant="normal">D</mi><mo>]</mo><mo>​</mo></mrow><mrow><mo>[</mo><mi mathvariant="normal">A</mi><mo>]</mo><mo>[</mo><mi mathvariant="normal">B</mi><mo>]</mo></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><msub><mi mathvariant="normal">K</mi><mfenced><mi>eq</mi></mfenced></msub><mo>=</mo><mfrac><mrow><mn>2</mn><mo>×</mo><mn>2</mn></mrow><mrow><mn>2</mn><mo>×</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mn>1</mn></math></p></div>


tags: ['Physics', 'Thermal Properties of Matter', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch0.db
title:
0.5 mole of an ideal gas at constant temperature 2 7 â C kept inside a cylinder of length L and crosssection area A closed by a massless piston. The cylinder is attached with a conducting rod of length L , cross-section area ( 1/9 ) m 2 and thermal conductivity k , whose other end is maintained at 0 â C . If piston is moved such that rate of heat flow through the conducing rod is constant then velocity of piston when it is at height L /2 from the bottom of cylinder is : [Neglect any kind of heat loss from system

slug:
0-5-mole-of-an-ideal-gas-at-constant-temperature-2-7-c-kept-inside-a-cylinder-of-length-l-and-cr-41784

question:
<div class="question">0.5 mole of an ideal gas at constant temperature $27^{\circ} \mathrm{C}$ kept inside a cylinder of length $L$ and crosssection area A closed by a massless piston.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/-iowH4MfsQxjSAxWlKQFCRBmNPye5ME0xQT28-7P41c.original.fullsize.png"/><br/> <br/> <br/>The cylinder is attached with a conducting rod of length $L,$ cross-section area $(1 / 9) \mathrm{m}^{2}$ and thermal conductivity $\mathrm{k}$, whose other end is maintained at $0^{\circ} \mathrm{C}$. If piston is moved such that rate of heat flow through the conducing rod is constant then velocity of piston when it is at height $L / 2$ from the bottom of cylinder is :
<br/> <br/>[Neglect any kind of heat loss from system</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\left(\frac{\mathrm{k}}{R}\right) \mathrm{m} / \mathrm{sec}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\left(\frac{\mathrm{k}}{10 R}\right) \mathrm{m} / \mathrm{sec}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\left(\frac{\mathrm{k}}{100 R}\right) \mathrm{m} / \mathrm{sec}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\left(\frac{\mathrm{k}}{1000 R}\right) \mathrm{m} / \mathrm{sec}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(\frac{\mathrm{k}}{100 R}\right) \mathrm{m} / \mathrm{sec}$</span> </div>

answer:
<div class="solution">$\frac{\Delta Q}{\Delta t}=\frac{\Delta W}{\Delta t}=$ work done per unit time = $\frac{\mathrm{k} a \theta}{L}$
<br/> <br/>$$
<br/> <br/>\frac{d W}{d t}=P \frac{d v}{d t}=\mathrm{k} \frac{a \theta}{L}, P=\frac{n R T}{V}
<br/> <br/>$$
<br/> <br/>$\Rightarrow \quad \frac{0.5 R(300)}{V} A \cdot \frac{d \ell}{d t}=\frac{\mathrm{k} a \theta}{L}$
<br/> <br/>$$
<br/> <br/>\Rightarrow \frac{0.5 R(300)}{A \cdot \frac{L}{2}} A \cdot v=\frac{\mathrm{k} a \theta}{L}
<br/> <br/>$$
<br/> <br/>$\Rightarrow \quad v=\frac{\mathrm{k} a}{R}\left(\frac{27}{300}\right)=\frac{\mathrm{k}}{100 R}$</div>


title: \(10^n+3\left(4^{n+2}\right)+5\) is divisible by \((n \in N)\)
slug: 10-n-3-left-4-n-2-right-5-is-divisible-by-n-in-n-27422
question: <div class="question">\(10^n+3\left(4^{n+2}\right)+5\) is divisible by \((n \in N)\)</div>
tags: ['Mathematics', 'Quadratic Equation', 'BITSAT', 'BITSAT 2009']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">9</span> </div>
source_db: MarksBatch0.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">7</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">5</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">9</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">17</span> </li> </ul>

answer:
<div class="solution">\(\begin{aligned}<br/>&amp; 10^n+3\left(4^{n+2}\right)+5 \text { Taking } n=2, \\<br/>&amp; 10^2+3 \times 4^4+5=100+768+5=873<br/>\end{aligned}\)<br/>Therefore this is divisible by 9.</div>


tags: ['Physics', 'Atomic Physics', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch0.db
title:
12 eV energy is given to electron in third orbit of H -atom, then final energy of electron when it ionise from third orbit, is

slug:
12-ev-energy-is-given-to-electron-in-third-orbit-of-h-atom-then-final-energy-of-electron-when-it-i-35461

question:
<div class="question"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo> </mo><mi>eV</mi></math> energy is given to electron in third orbit of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">H</mi></math>-atom, then final energy of electron when it ionise from third orbit, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>.</mo><mn>25</mn><mo> </mo><mi>eV</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>.</mo><mn>49</mn><mo> </mo><mi>eV</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo> </mo><mi>eV</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn><mo>.</mo><mn>15</mn><mo> </mo><mi>eV</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>.</mo><mn>49</mn><mo> </mo><mi>eV</mi></math></span> </div>

answer:
<div class="solution"><p>Given, total energy given to electron in third orbit,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mn>12</mn><mo> </mo><mi>eV</mi></math></p><p>Energy of third orbit of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">H</mi></math>-atom, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>'</mo><mo>=</mo><mfrac><mrow><mo>-</mo><mn>13</mn><mo>.</mo><mn>6</mn></mrow><msup><mi>n</mi><mn>2</mn></msup></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mo>-</mo><mn>13</mn><mo>.</mo><mn>6</mn></mrow><msup><mn>3</mn><mn>2</mn></msup></mfrac><mo>=</mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>51</mn><mo> </mo><mi>eV</mi></math></p><p>lonisation energy of electron of third orbit, <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>E</mi><mrow><mo>'</mo><mo>'</mo></mrow></msup><mo>=</mo><mo>-</mo><mi>E</mi><mo>'</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>-</mo><mfenced><mrow><mo>-</mo><mn>1</mn><mo>.</mo><mn>51</mn><mo> </mo><mi>eV</mi></mrow></mfenced><mo>⇒</mo><msup><mi>E</mi><mrow><mo>'</mo><mo>'</mo></mrow></msup><mo>=</mo><mn>1</mn><mo>.</mo><mn>51</mn><mo> </mo><mi>eV</mi></math></p><p>Hence, final energy of electron when it comes out of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">H</mi></math>-atom from third orbit</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>E</mi><mi>f</mi></msub><mo>=</mo><mi>E</mi><mo>-</mo><msup><mi>E</mi><mrow><mo>'</mo><mo>'</mo></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>12</mn><mo>-</mo><mn>1</mn><mo>.</mo><mn>51</mn><mo>=</mo><mn>10</mn><mo>.</mo><mn>49</mn><mo> </mo><mi>eV</mi></math></p></div>


tags: ['Chemistry', 'General Organic Chemistry', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch0.db
title:
0.20 g of an organic compound gave 0.12 g of AgBr By using Carius method, the percentage of bromine in the compound will be

slug:
0-20-g-of-an-organic-compound-gave-0-12-g-of-agbr-by-using-carius-method-the-percentage-of-bromine-27668

question:
<div class="question">$0.20 \mathrm{~g}$ of an organic compound gave $0.12 \mathrm{~g}$ of AgBr By using Carius method, the percentage of bromine in the compound will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>$34.06 \%$
<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>$44.04 \%$
<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>$54 \%$
<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"> <br/>$25 \%$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>$25 \%$</span> </div>

answer:
<div class="solution">Given,
<br/>Mass of an organic compound $=0.20 \mathrm{~g}$
<br/>Mass of $\mathrm{AgBr}=0.12 \mathrm{~g}$
<br/>Molecular mass of $\mathrm{AgBr}=188 \mathrm{~g} \mathrm{~mol}^{-1}$
<br/>$188 \mathrm{~g}$ of AgBr contains $80 \mathrm{~g}$ of bromine
<br/>$\therefore 0.12 \mathrm{~g}$ of $\mathrm{AgBr}$ will contain $=\frac{80}{188} \times 0.12$
<br/>$=0.05 \mathrm{~g}$ of bromine
<br/>$\therefore$ Percentage of bromine $=\frac{0.05}{0.20} \times 100$
<br/>$=25 \%$</div>


title: 2,4 -Dichlorophenoxyacetic add is used as
slug: 2-4-dichlorophenoxyacetic-add-is-used-as-14583
question: <div class="question">2,4 -Dichlorophenoxyacetic add is used as</div>
tags: ['Chemistry', 'Chemistry in Everyday Life', 'BITSAT', 'BITSAT 2012']
answer: <div class="solution">2,4 -dichlorophenoxyacetic acid is used as a herbicide.</div>
source_db: MarksBatch0.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Fungicide</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Insecticide</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Herbicide</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Moth repellant</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Herbicide</span> </div>


tags: ['Chemistry', 'Redox Reactions', 'BITSAT', 'BITSAT 2012']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch0.db
title:
0.45 g of acid molecular weight 90 is neutralised by 20 ml of 0.5 N caustic potash. The basicity of acid is

slug:
0-45-g-of-acid-molecular-weight-90-is-neutralised-by-20-ml-of-0-5-n-caustic-potash-the-basicity-of-63219

question:
<div class="question">$0.45 \mathrm{~g}$ of acid molecular weight 90 is neutralised by $20 \mathrm{ml}$ of $0.5 \mathrm{~N}$ caustic potash. The basicity of acid is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">2</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">3</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">4</span> </li> </ul>

answer:
<div class="solution">Eq. of acid = Eq of base,
<br/>$\begin{array}{l}
<br/>\therefore \frac{0.45}{\mathrm{E} \cdot \mathrm{wt}}=\frac{20 \times 0.5}{1000}=\mathrm{E} \mathrm{wt}=45 \\
<br/>\text { Basicity }=\frac{\mathrm{M} \cdot \mathrm{wt}}{\mathrm{E} \cdot \mathrm{wt}}=\frac{90}{45}=2
<br/>\end{array}$</div>


slug: 1-00-g-of-a-non-electrolyte-solute-molar-mass-250-g-mol-1-was-dissolved-in-51-2-g-of-benzene-43357
tags: ['Chemistry', 'Solutions', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch0.db
title:
1.00 g of a non-electrolyte solute (molar mass 250 g mol â 1 ) was dissolved in 51.2 g of benzene. If the freezing point depression constant, K f â of benzene is 5.12 K kg mol â 1 , the freezing point of benzene will be lowered by

question:
<div class="question">$1.00 \mathrm{~g}$ of a non-electrolyte solute (molar mass $\left.250 \mathrm{~g} \mathrm{~mol}^{-1}\right)$ was dissolved in $51.2 \mathrm{~g}$ of benzene. If the freezing point depression constant, $\mathrm{K}_{\mathrm{f}}$ of benzene is $5.12 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$, the freezing point of benzene will be lowered by</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.3 \mathrm{~K}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.5 \mathrm{~K}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$0.4 \mathrm{~K}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">0.2</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.4 \mathrm{~K}$</span> </div>

answer:
<div class="solution">$\Delta \mathrm{T}_{\mathrm{f}}=\mathrm{K}_{\mathrm{f}} \mathrm{m}=5.12 \times \frac{1}{250} \times \frac{1000}{51.2}=0.4 \mathrm{~K}$</div>


slug: 100-ml-of-2-m-of-formic-acid-p-k-a-3-74-is-neutralise-by-naoh-at-the-equivalence-point-p-69498
tags: ['Chemistry', 'Ionic Equilibrium', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch0.db
title:
100 mL of 2 M of formic acid ( p K a â = 3.74 ) is neutralise by NaOH , at the equivalence point pH is

question:
<div class="question">$100 \mathrm{~mL}$ of $2 \mathrm{M}$ of formic acid $\left(\mathrm{p} K_a=3.74\right)$ is neutralise by $\mathrm{NaOH}$, at the equivalence point $\mathrm{pH}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>$7$
<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>$6$
<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>$9.5$
<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"> <br/>$8.87$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>$8.87$</span> </div>

answer:
<div class="solution">Sodium formate is present at the equivalence point. It is the salt of weak acid $+$ strong base. So, final solution will be basic in nature.
<br/>As we know
<br/>$\mathrm{pH}=7+\frac{\mathrm{p} K_a}{2}+\frac{\log C}{2}$
<br/>where, $C$ is concentration of salt.
<br/>Total volume of solution $=100+100=200 \mathrm{~mL}$
<br/>Concentration of salt $(C)=2 \times \frac{100}{200}=1 \mathrm{M}$
<br/>$\mathrm{pH}=7+\frac{3.74}{2}+\frac{\log [1]}{2}$
<br/>$\mathrm{pH}=7+1.87+0$
<br/>$\mathrm{pH}=8.87$</div>


slug: 107-u-and-v-are-two-non-collinear-unit-vectors-such-that-2-u-v-u-v-26847
tags: ['Mathematics', 'Vector Algebra', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch0.db
title:
107. u ^ and v ^ are two non-collinear unit vectors such that â 2 u ^ + v ^ â + u ^ Ã v ^ â = 1 . Then the value of â£ u ^ Ã v ^ â£ is equal to

question:
<div class="question">107. $\hat{\mathbf{u}}$ and $\hat{\mathbf{v}}$ are two non-collinear unit vectors such that $\left|\frac{\hat{\mathbf{u}}+\hat{\mathbf{v}}}{\mathbf{2}}+\hat{\mathbf{u}} \times \hat{\mathbf{v}}\right|=1$. Then the value of $|\hat{\mathbf{u}} \times \hat{\mathbf{v}}|$ is equal to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>$\left|\frac{\hat{\mathbf{u}}+\hat{\mathbf{v}}}{2}\right|$
<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>$|\hat{\mathbf{u}}+\hat{\mathbf{v}}|$
<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>$|\hat{\mathbf{u}}-\hat{\mathbf{v}}|$
<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"> <br/>$\left|\frac{\hat{\mathbf{u}}-\hat{\mathbf{v}}}{2}\right|$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>$\left|\frac{\hat{\mathbf{u}}-\hat{\mathbf{v}}}{2}\right|$</span> </div>

answer:
<div class="solution">Given that, $\left|\frac{\hat{\mathbf{u}}+\hat{\mathbf{v}}}{2}+\hat{\mathbf{u}} \times \hat{\mathbf{v}}\right|=1$
<br/>$$
<br/>\begin{array}{ll}
<br/>\Rightarrow &amp; \left|\frac{\hat{\mathbf{u}}+\hat{\mathbf{v}}}{2}+\hat{\mathbf{u}} \times \hat{\mathbf{v}}\right|^2=1 \\
<br/>\Rightarrow &amp; \frac{2+2 \cos \theta}{4}+\sin ^2 \theta=1 \\
<br/> &amp; \quad[\because \hat{\mathbf{u}} \cdot(\hat{\mathbf{u}} \times \hat{\mathbf{v}})=\hat{\mathbf{v}}(\hat{\mathbf{u}} \times \hat{\mathbf{v}})=0] \\
<br/>\Rightarrow &amp; \cos ^2 \frac{\theta}{2}=\cos 2 \theta \\
<br/>\Rightarrow &amp; \theta=n \pi \pm \frac{\theta}{2}, n \in z \\
<br/>\Rightarrow &amp; \theta=\frac{2 \pi}{3}
<br/>\end{array}
<br/>$$
<br/>$\Rightarrow \quad|\hat{\mathbf{u}} \times \hat{\mathbf{v}}|=\sin \frac{2 \pi}{3}=\sin \frac{\pi}{3}=\left|\frac{\hat{\mathbf{u}}-\hat{\mathbf{v}}}{2}\right|$</div>


slug: 1-25-g-of-a-sample-of-na-2-co-3-and-na-2-so-4-is-dissolved-in-250-ml-solution-25-ml-70403
tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch0.db
title:
1.25 g of a sample of Na 2 â CO 3 â and Na 2 â SO 4 â is dissolved in 250 ml solution. 25 ml of this solution neutralises 20 ml of 0.1 N H 2 â SO 4 â . The % of Na 2 â CO 3 â in this sample is

question:
<div class="question">$1.25 \mathrm{~g}$ of a sample of $\mathrm{Na}_{2} \mathrm{CO}_{3}$ and $\mathrm{Na}_{2} \mathrm{SO}_{4}$ is
<br/> <br/>dissolved in $250 \mathrm{ml}$ solution. $25 \mathrm{ml}$ of this solution neutralises $20 \mathrm{ml}$ of $0.1 \mathrm{~N} \mathrm{H}_{2} \mathrm{SO}_{4}$. The $\%$ of $\mathrm{Na}_{2} \mathrm{CO}_{3}$
<br/> <br/>in this sample is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$84.8 \%$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$8.48 \%$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$15.2 \%$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$42.4 \%$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$84.8 \%$</span> </div>

answer:
<div class="solution">Let the amount of $\mathrm{Na}_{2} \mathrm{CO}_{3}$ present in the mixture be $\mathrm{xg} . \mathrm{Na}_{2} \mathrm{SO}_{4}$ will not react with $\mathrm{H}_{2} \mathrm{SO}_{4} .$ Then
<br/> <br/>$\frac{x}{53}=\frac{20 \times 0.1 \times 10}{1000} \therefore x=1.06 g$
<br/> <br/>$\therefore$ Percentage of $\mathrm{Na}_{2} \mathrm{CO}_{3}=$
<br/> <br/>$\frac{1.06 \times 100}{1.25}=84.8 \%$</div>


slug: 3-92-g-of-ferrous-ammonium-sulphate-react-completely-with-50-ml-10-n-kmno-4-solution-the-pe-41909
tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'BITSAT', 'BITSAT 2014']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">50</span> </div>
source_db: MarksBatch0.db
title:
3.92 g of ferrous ammonium sulphate react completely with 50 ml 10 N â KMnO 4 â solution. The percentage purity of the sample is

question:
<div class="question">$3.92 \mathrm{~g}$ of ferrous ammonium sulphate react completely with $50 \mathrm{ml} \frac{\mathrm{N}}{10} \mathrm{KMnO}_{4}$ solution. The percentage purity of the sample is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">50</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">78.4</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">80</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">39.2</span> </li> </ul>

answer:
<div class="solution">Eq of $\mathrm{KMnO}_{4}$ used $=\frac{50 \times 1}{1000 \times 10}=0.005$
<br/> <br/>$\therefore$ Eq of FAS reacted $=0.005$
<br/> <br/>$\therefore$ weight of FAS needed
<br/> <br/>$$
<br/> <br/>=0.005 \times 392=1.96 \mathrm{~g}
<br/> <br/>$$
<br/> <br/>Thus percentage purity of FAS is $50 \%$</div>


tags: ['Chemistry', 'Redox Reactions', 'BITSAT', 'BITSAT 2011']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">9</span> </div>
source_db: MarksBatch0.db
title:
1.520 g of hydroxide of a metal on ignition gave 0.995 g of oxide. The equivalent weight of metal is:

slug:
1-520-g-of-hydroxide-of-a-metal-on-ignition-gave-0-995-g-of-oxide-the-equivalent-weight-of-metal-is-46725

question:
<div class="question">$1.520 \mathrm{~g}$ of hydroxide of a metal on ignition gave $0.995 \mathrm{~g}$ of oxide. The equivalent weight of metal is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1.52</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">0.995</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">190</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">9</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">Let $E$ be the equivalent weight of the metal<br/>$$<br/>\text { So, } \frac{E+17}{E+8}=\frac{1.52}{0.995}<br/>$$<br/>[17 is equivalent weight of $\mathrm{OH}$ and 8 is equivalent weight of oxygen]<br/>$$<br/>\begin{array}{l}<br/>\Rightarrow 0.995 \mathrm{E}+17 \times 0.995=\mathrm{E} \times 1.52+8 \times 1.52 \\<br/>\Rightarrow 0.525 \mathrm{E}=16.915-12.16=4.755 \\<br/>\therefore \quad \mathrm{E}=\frac{4.755}{0.525}=9<br/>\end{array}<br/>$$</div>


tags: ['Physics', 'Oscillations', 'BITSAT', 'BITSAT 2016']
answer: <div class="solution">No Solution</div>
source_db: MarksBatch0.db
title:
A 1 kg mass is attached to a spring of force constant 600 N / m and rests on a smooth horizontal surface with other end of the spring tied to wall as shown in figure. A second mass of 0.5 kg slides along the surface towards the first at 3 m / s . If the masses make a perfectly inelastic collision, then find amplitude and time period of oscillation of combined mass.

slug:
a-1-kg-mass-is-attached-to-a-spring-of-force-constant-600-n-m-and-rests-on-a-smooth-horizontal-sur-22713

question:
<div class="question">A $1 \mathrm{~kg}$ mass is attached to a spring of force constant $600 \mathrm{~N} / \mathrm{m}$ and rests on a smooth horizontal surface with other end of the spring tied to wall as shown in figure. A second mass of $0.5 \mathrm{~kg}$ slides along the surface towards the first at $3 \mathrm{~m} / \mathrm{s}$. If the masses make a perfectly inelastic collision, then find amplitude and time period of oscillation of combined mass.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/7RB8kg5GImmHiuCU5XdGpoGOppt6O5xpyJtDsUB4MYA.original.fullsize.png"/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$5 \mathrm{~cm}, \frac{\pi}{10} \mathrm{~s}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$5 \mathrm{~cm}, \frac{\pi}{5} \mathrm{~s}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$4 \mathrm{~cm}, \frac{2 \pi}{5} \mathrm{~s}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$4 \mathrm{~cm}, \frac{\pi}{3} \mathrm{~s}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$5 \mathrm{~cm}, \frac{\pi}{10} \mathrm{~s}$</span> </div>


slug: a-2-m-wide-truck-is-moving-with-a-uniform-speed-v-0-8-m-s-along-a-straight-horizontal-road-97177
tags: ['Physics', 'Motion In Two Dimensions', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch0.db
title:
A 2 m wide truck is moving with a uniform speed v 0 â = 8 m / s along a straight horizontal road. A pedestrain starts to cross the road with a uniform speed v when the truck is 4 m away from him. The minimum value of v so that he can cross the road safely is

question:
<div class="question">A $2 \mathrm{~m}$ wide truck is moving with a uniform speed $v_{0}=8 \mathrm{~m} / \mathrm{s}$ along a straight horizontal road. $\mathrm{A}$ pedestrain starts to cross the road with a uniform speed $v$ when the truck is 4 m away from him. The minimum value of $v$ so that he can cross the road safely is
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/Z3fJLaj1dg6v6X8HIQc2GSDfUqbDQP6LBa9-0HbyYFE.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2.62 \mathrm{~m} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$4.6 \mathrm{~m} / \mathrm{s}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$3.57 \mathrm{~m} / \mathrm{s}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1.414 \mathrm{~m} / \mathrm{s}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$3.57 \mathrm{~m} / \mathrm{s}$</span> </div>

answer:
<div class="solution">Let the man starts crossing the road at an angle $\theta$ as shown in figure. For safe crossing the condition is that the man must cross the road by the time the truck describes the distance 4 à¥¤ $A C$ or 4 à¥¤ $2 \cot \theta$. $\therefore \frac{4+2 \cot \theta}{8}=\frac{2 / \sin \theta}{v}$ or $v=\frac{8}{2 \sin \theta+\cos \theta}$
<br/> <br/>For minimum $v, \frac{d v}{d \theta}=0$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/0Fx5hXOh-RW30FnSsjhaGPlflHon3wkCwFFKFHGt6w4.original.fullsize.png"/><br/> <br/> <br/>or $\frac{-8(2 \cos \theta-\sin \theta)}{(2 \sin \theta+\cos \theta)^{2}}=0$ or $2 \cos \theta-$
<br/> <br/>$\sin \theta=0$
<br/> <br/>or $\tan \theta=2$
<br/> <br/>From equation (i),
<br/> <br/>$$
<br/> <br/>v_{\min }=\frac{8}{2\left(\frac{2}{\sqrt{5}}\right)+\frac{1}{\sqrt{5}}}=\frac{8}{\sqrt{5}}=3.57 \mathrm{~m} / \mathrm{s}
<br/> <br/>$$</div>


slug: a-4-x-8-x-4-x-2-1-d-x-2-0-4-x-8-x-4-x-2-1-d-x-then-a-99247
tags: ['Mathematics', 'Definite Integration', 'BITSAT', 'BITSAT 2021']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch0.db
title:
â« â a 4 â ( x 8 â x 4 + x 2 + 1 ) d x = 2 â« 0 4 â ( x 8 â x 4 + x 2 + 1 ) d x then a =

question:
<div class="question">$\int_{-a}^{4}\left(x^{8}-x^{4}+x^{2}+1\right) d x=2 \int_{0}^{4}\left(x^{8}-x^{4}+x^{2}+1\right) d x$ then $a=$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">3</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">4</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">6</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">8</span> </li> </ul>

answer:
<div class="solution">If $\mathrm{f}(x)$ is an even function then
<br/> <br/>$\int_{-a}^{a} f(x) d x=2 \int_{0}^{a} f(x) d x$
<br/> <br/>Here $\mathrm{f}(x)=x^{8}-x^{4}+x^{2}+1$ is an even function, therefore $a=4$.</div>


tags: ['Chemistry', 'Solutions', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch0.db
title:
A 0.5 molal solution of ethylene glycol in water is used as coolant in a car. If the freezing point constant of water be 1.8 6 â C per mole, the mixture shall freeze at

slug:
a-0-5-molal-solution-of-ethylene-glycol-in-water-is-used-as-coolant-in-a-car-if-the-freezing-point-79884

question:
<div class="question">A 0.5 molal solution of ethylene glycol in water is used as coolant in a car. If the freezing point constant of water be $1.86^{\circ} \mathrm{C}$ per mole, the mixture shall freeze at</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.93^{\circ} \mathrm{C}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$-0.93^{\circ} \mathrm{C}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1.86^{\circ} \mathrm{C}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-1.86^{\circ} \mathrm{C}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-0.93^{\circ} \mathrm{C}$</span> </div>

answer:
<div class="solution"><br/>$\begin{aligned} &amp;\Delta T_f=K_f \times m=1.86 \times 0.5=0.93^{\circ} \mathrm{C} \text {; } \\ &amp; T_f=-0.93^{\circ} \mathrm{C}\end{aligned}$</div>


tags: ['Physics', 'Electromagnetic Induction', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch0.db
title:
A 12 V battery connected to a coil of resistance 6Î© through a switch, drives a constant current in the circuit. The switch is opened in 1 ms . The emf induced across the coil is 20 V . The inductance of the coil is :

slug:
a-12-v-battery-connected-to-a-coil-of-resistance-6-through-a-switch-drives-a-constant-current-in-83587

question:
<div class="question">A $12 \mathrm{~V}$ battery connected to a coil of resistance $6 \Omega$ through a switch, drives a constant current in the circuit. The switch is opened in $1 \mathrm{~ms}$. The emf induced across the coil is $20 \mathrm{~V}$. The inductance of the coil is :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$5 \mathrm{mH}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$12 \mathrm{mH}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$8 \mathrm{mH}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$10 \mathrm{mH}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$10 \mathrm{mH}$</span> </div>

answer:
<div class="solution">Induced emf, $\varepsilon=-\mathrm{L} \frac{\mathrm{dI}}{\mathrm{dt}} \Rightarrow 20=-\mathrm{L} \frac{(0-2)}{10^{-3}}$ Hence, inductance of the coil.<br/>$\mathrm{L}=10 \mathrm{mH}$</div>


slug: a-100-m-long-wire-having-cross-sectional-area-6-25-1-0-4-m-2-and-young-s-modulus-is-1-0-10-nm-56856
tags: ['Physics', 'Mechanical Properties of Solids', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch0.db
title:
A 100 m long wire having cross-sectional area 6.25 Ã 1 0 â 4 m 2 and Young's modulus is 1 0 10 Nm â 2 is subjected to a load of 250 N , then the elongation in the wire will be :

question:
<div class="question">A $100 \mathrm{~m}$ long wire having cross-sectional area $6.25 \times 10^{-4} \mathrm{~m}^2$ and Young's modulus is $10^{10}$ $\mathrm{Nm}^{-2}$ is subjected to a load of $250 \mathrm{~N}$, then the elongation in the wire will be :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$6.25 \times 10^{-3} \mathrm{~m}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$4 \times 10^{-4} \mathrm{~m}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$6.25 \times 10^{-6} \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$4 \times 10^{-3} \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$4 \times 10^{-3} \mathrm{~m}$</span> </div>

answer:
<div class="solution">$\Delta \ell=\frac{F \ell}{Y A}=\frac{250 \times 100}{10^{10} \times 6.25 \times 10^{-4}}=40 \times 10^{-4} \mathrm{~m}$<br/>$=4 \times 10^{-3} \mathrm{~m}$</div>


tags: ['Physics', 'Atomic Physics', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch0.db
title:
A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:

slug:
a-12-5-ev-electron-beam-is-used-to-bombard-gaseous-hydrogen-at-room-temperature-the-number-of-spect-55174

question:
<div class="question">A $12.5 \mathrm{eV}$ electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">1</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">3</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">4</span> </li> </ul>

answer:
<div class="solution">If we assume electron in hydrogen atom takes energy $12.09 \mathrm{eV}$ from the incoming radiation, the maximum excited state of electron will be $n=3$. So, number of spectral lines is $\frac{3(3-1)}{2}=3$.<br/>Here we assume some part of energy $12.5 \mathrm{eV}$ $-12.09 \mathrm{eV}=0.41 \mathrm{eV}$ get lost due to collision.</div>


tags: ['Physics', 'Work Power Energy', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch0.db
title:
A 3.628 kg freight car moving along a horizontal rail road spur track at 7.2 km / hour strikes a bumper whose coil springs experiences a maximum compression of 30 cm in stopping the car. The elastic potential energy of the springs at the instant when they are compressed 15 cm is

slug:
a-3-628-kg-freight-car-moving-along-a-horizontal-rail-road-spur-track-at-7-2-km-hour-strikes-a-bum-33470

question:
<div class="question">A $3.628 \mathrm{~kg}$ freight car moving along a horizontal rail road spur track at $7.2 \mathrm{~km} /$ hour strikes a bumper whose coil springs experiences a maximum compression of $30 \mathrm{~cm}$ in stopping the car. The elastic potential energy of the springs at the instant when they are compressed $15 \mathrm{~cm}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$12.1 \times 10^{4} \mathrm{~J}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$121 \times 10^{4} \mathrm{~J}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$1.21 \times 10^{4} \mathrm{~J}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1.21 \times 10^{6} \mathrm{~J}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1.21 \times 10^{4} \mathrm{~J}$</span> </div>

answer:
<div class="solution">\(\begin{aligned} 7.2 \mathrm{~km} / \mathrm{ram} &amp;=\frac{7.2 \times \frac{5}{18} \mathrm{~m} / \mathrm{s}}{7 / 2^{2}} \\ &amp;=\frac{72 \times 5}{10 \times 18}=2 \mathrm{~m} / \mathrm{s} \end{aligned}\)
<br/> <br/>firt case EC \(\frac{1}{2} k x^{2}=\frac{1}{2} m v^{2}\) \(\Rightarrow \frac{1}{7} k\left(30 \times 10^{-2}\right)^{2}=\frac{1}{2} \times 3.628 \times(2)^{2}\) \(k=\frac{4 \times 3.628}{9 \times 10^{-2}}\)
<br/> <br/>\(\begin{aligned} \text { EC } &amp; \frac{1}{2} k x^{2}=\frac{1}{2} m v^{2} \\ \Rightarrow &amp; \frac{1}{2} k\left(30 \times 10^{-2}\right)^{2}=\frac{1}{2} \times 3.628 \times(2)^{2} \\ k &amp;=\frac{4 \times 3.628}{9 \times 10^{-2}} \end{aligned}\)
<br/> <br/>energy potential enrgy when conpressed at \(15 \mathrm{~cm}\) 
<br/> <br/>\(\begin{aligned}\Rightarrow &amp; \frac{1}{2} k\left(15 \times 10^{-2}\right)^{2} \\=&amp; \frac{1}{2} \times \frac{4 \times 3.628}{9 \times 10^{-2}} \times 225 \times 10^{-4} \\=&amp; \frac{1639 \times 10^{-2}}{9} \\=&amp; 182.206 \times 10^{-2} \end{aligned}\)
<br/> <br/>\(\begin{aligned} &amp;\Rightarrow \frac{1}{2} k\left(15 \times 10^{2}\right. \\ &amp;=\frac{1}{2} \times \frac{\alpha \times 3.628}{9 \times 10^{-2}} \times 225 \times 10^{-4} \\ &amp;=\frac{1639 \times 10^{-2}}{9} \\ &amp;=182.206 \times 10^{-2} \end{aligned}\)</div>


slug: a-bag-contains-2-n-1-coins-it-is-known-that-n-of-these-coins-have-a-head-on-both-sides-where-70477
tags: ['Mathematics', 'Probability', 'BITSAT', 'BITSAT 2015']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">10</span> </div>
source_db: MarksBatch0.db
title:
A bag contains ( 2 n + 1 ) coins. It is known that n of these coins have a head on both sides, whereas the remaining ( n + 1 ) coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is 31/42 , then n is equal to

question:
<div class="question">A bag contains $(2 n+1)$ coins. It is known that n of these coins have a head on both sides, whereas the remaining $(\mathrm{n}+1)$ coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is $31 / 42,$ then $\mathrm{n}$ is equal to</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">10</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">11</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">12</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">13</span> </li> </ul>

answer:
<div class="solution">Total number of coins $=2 \mathrm{n}+1$
<br/> <br/>Consider the following events:
<br/> <br/>$\mathrm{E}_{1}=$ Getting a coin having head on both
<br/> <br/>sides from the bag.
<br/> <br/>$\mathrm{E}_{2}=$ Getting a fair coin from the bag
<br/> <br/>$\mathrm{A}=$ Toss results in a head
<br/> <br/>Given: $\mathrm{P}(\mathrm{A})=\frac{31}{42}, \mathrm{P}\left(\mathrm{E}_{1}\right)=\frac{\mathrm{n}}{2 \mathrm{n}+1}$
<br/> <br/>and $\mathrm{P}\left(\mathrm{E}_{2}\right)=\frac{\mathrm{n}+1}{2 \mathrm{n}+1}$
<br/> <br/>Then,
<br/> <br/>$\mathrm{P}(\mathrm{A})=\mathrm{P}\left(\mathrm{E}_{1}\right) \mathrm{P}\left(\mathrm{A} / \mathrm{E}_{1}\right)+\mathrm{P}\left(\mathrm{E}_{2}\right) \mathrm{P}\left(\mathrm{A} / \mathrm{E}_{2}\right)$
<br/> <br/>$\Rightarrow \frac{31}{42}=\frac{n}{2 n+1} \times 1+\frac{n+1}{2 n+1} \times \frac{1}{2}$
<br/> <br/>$\frac{31}{42}=\frac{n}{2 n+1}+\frac{n+1}{2(2 n+1)}$
<br/> <br/>$\Rightarrow \frac{31}{42}=\frac{3 n+1}{2(2 n+1)}$
<br/> <br/>$\Rightarrow \frac{31}{21}=\frac{3 n+1}{2 n+1}$
<br/> <br/>$n=10$</div>


tags: ['Mathematics', 'Probability', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch0.db
title:
A bag contains 3 red and 3 white balls. Two balls are drawn one by one. The probability that they are of different colours is.

slug:
a-bag-contains-3-red-and-3-white-balls-two-balls-are-drawn-one-by-one-the-probability-that-they-ar-88773

question:
<div class="question">A bag contains 3 red and 3 white balls. Two balls are drawn one by one. The probability that they are of different colours is.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$3 / 10$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 / 5$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$3 / 5$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$3 / 5$</span> </div>

answer:
<div class="solution">Let $\mathrm{A} \equiv$ event that drawn ball is red $\mathrm{B} \equiv$ event that drawn ball is white Then $\mathrm{AB}$ and $\mathrm{BA}$ are two disjoint cases of the given event.
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\therefore P(A B+B A)=P(A B)+P(B A) \\
<br/> <br/>=P(A) \quad P\left(\frac{B}{A}\right)+P(B) \quad P\left(\frac{A}{B}\right)
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>$=\frac{3}{6} \cdot \frac{3}{5}+\frac{3}{6} \cdot \frac{3}{5}=\frac{3}{5}$</div>


tags: ['Mathematics', 'Probability', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch0.db
title:
A bag contains 5 brown and 4 white socks. A man pulls out 2 socks. Find the probability that they are of the same colour.

slug:
a-bag-contains-5-brown-and-4-white-socks-a-man-pulls-out-2-socks-find-the-probability-that-they-ar-67027

question:
<div class="question">A bag contains 5 brown and 4 white socks. $A$ man pulls out 2 socks. Find the probability that they are of the same colour.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{4}{9}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{2}{9}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{5}{9}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{7}{9}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{4}{9}$</span> </div>

answer:
<div class="solution">Let $A \equiv$ event of two socks being brown. $\mathrm{B} \equiv$ event of two socks being white.
<br/> <br/>$$
<br/> <br/>\text { Then } \begin{aligned}
<br/> <br/>&amp; P(A)=\frac{{ }^{5} C_{2}}{{ }^{9} C_{2}}=\frac{5.4}{9.8}=\frac{5}{18}, \mathrm{P}(\mathrm{B}) \\
<br/> <br/>&amp;=\frac{{ }^{4} \mathrm{C}_{2}}{{ }^{9} \mathrm{C}_{2}}=\frac{4.3}{9.8}=\frac{3}{18}
<br/> <br/>\end{aligned}
<br/> <br/>$$
<br/> <br/>Now, since $\mathrm{A}$ and $\mathrm{B}$ are mutually exclusive events, so required probability
<br/> <br/>$$
<br/> <br/>=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})=\frac{5}{18}+\frac{3}{18}=\frac{4}{9}
<br/> <br/>$$</div>


tags: ['Mathematics', 'Probability', 'BITSAT', 'BITSAT 2014']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch0.db
title:
A bag contains n + 1 coins. It is known that one of these coins shows heads on both sides, whereas the other coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is 12 7 â , then the value of n is.

slug:
a-bag-contains-n-1-coins-it-is-known-that-one-of-these-coins-shows-heads-on-both-sides-whereas-t-95325

question:
<div class="question">A bag contains $n+1$ coins. It is known that one of these coins shows heads on both sides, whereas the other coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is $\frac{7}{12},$ then the value of $n$ is.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">3</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">4</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">5</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

answer:
<div class="solution">Let $E_{1}$ denote the event "a coin with head on both sides is selected" and $\mathrm{E}_{2}$ denotes the event " a fair coin is selected". Let $A$ be
<br/> <br/>the event " he toss, results in heads".
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\therefore \mathrm{P}\left(\mathrm{E}_{1}\right)=\frac{1}{n+1}, \mathrm{P}\left(\mathrm{E}_{2}\right)=\frac{n}{n+1} \text { and } \\
<br/> <br/>\mathrm{P}\left(\frac{\mathrm{A}}{\mathrm{E}_{1}}\right)=1, \mathrm{P}\left(\frac{\mathrm{A}}{\mathrm{E}_{2}}\right)=\frac{1}{2} \\
<br/> <br/>\therefore \mathrm{P}(\mathrm{A})=\mathrm{P}\left(\mathrm{E}_{1}\right) \mathrm{P}\left(\frac{\mathrm{A}}{\mathrm{E}_{1}}\right)+\mathrm{P}\left(\mathrm{E}_{2}\right) \mathrm{P}\left(\frac{\mathrm{A}}{\mathrm{E}_{2}}\right) \\
<br/> <br/>\Rightarrow \frac{7}{12}=\frac{1}{n+1} \times 1+\frac{n}{n+1} \times \frac{1}{2} \\
<br/> <br/>\Rightarrow 14 n+14=24+12 n \Rightarrow n=5
<br/> <br/>\end{array}
<br/> <br/>$$</div>


tags: ['Physics', 'Motion In One Dimension', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch0.db
title:
A ball is dropped vertically from a height d above the ground. It hits the ground and bounces up vertically to a height d / 2 . Neglecting subsequent motion and air resistance, its velocity v varies with height h above the ground as

slug:
a-ball-is-dropped-vertically-from-a-height-d-above-the-ground-it-hits-the-ground-and-bounces-up-ver-18987

question:
<div class="question">A ball is dropped vertically from a height <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math> above the ground. It hits the ground and bounces up vertically to a height <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>/</mo><mn>2</mn><mo>.</mo></math> Neglecting subsequent motion and air resistance, its velocity <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math> varies with height <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math> above the ground as</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/c9f34755-a0da-4eb7-88b7-7d64123d4824-image.png" style="width: 210px; height: 208px;"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/d7fd39e2-dd4c-41fd-acf8-efc69b8c9adf-image.png" style="width: 210px; height: 216px;"/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/a16d3a52-2ec5-4b81-af3b-f71233f03b6e-image.png" style="width: 210px; height: 219px;"/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/cf90d266-7e93-4f3c-acb2-0bf1599aaab5-image.png" style="width: 210px; height: 208px;"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/c9f34755-a0da-4eb7-88b7-7d64123d4824-image.png" style="width: 210px; height: 208px;"/></span> </div>

answer:
<div class="solution"><p>For the uniformly accelerated/decelcrated motion,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>v</mi><mn>2</mn></msup><mo>=</mo><msup><mi>u</mi><mn>2</mn></msup><mo>±</mo><mn>2</mn><mi>g</mi><mi>h</mi></math></p><p>So. from this equation. we can say <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>-</mo><mi>h</mi></math> paragraph is parabola.</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/9a271acb-9ff1-4c78-bc96-8aba42a9ec7d-image.png" style="width: 220px; height: 218px;"/></p><p>Initially, velocity is downwards <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>-</mo><mi>v</mi><mi>e</mi><mo>)</mo></math> after collision, it reverses the direction with smaller magnitude and velocity is upwards <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>-</mo><mi>v</mi><mi>e</mi><mo>)</mo></math>.</p><p>So. graph (a) satisfies these conditions.</p><p>Also, When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn><mo>,</mo><mo> </mo><mi>h</mi><mo>=</mo><mi>d</mi></math> Velocity increases downwards <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">U</mi><mo>→</mo><mi mathvariant="normal">A</mi><mo>)</mo></math></p><p>When <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>-</mo><mn>1</mn></math> velocity reverses its direction <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msup><mi>A</mi><mo>'</mo></msup><mo>→</mo><mi>B</mi></mrow></mfenced></math></p></div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch0.db
title:
A ball of mass 0.2 kg is thrown vertically upwards by applying a force by hand. If the hand moves 0.2 m while applying the force and the ball goes upto 2 m height further, find the magnitude of the force. (Consider g = 10 m / s 2 ) .

slug:
a-ball-of-mass-0-2-kg-is-thrown-vertically-upwards-by-applying-a-force-by-hand-if-the-hand-moves-0-93525

question:
<div class="question">A ball of mass $0.2 \mathrm{~kg}$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.2 \mathrm{~m}$ while applying the force and the ball goes upto $2 \mathrm{~m}$ height further, find the magnitude of the force. (Consider $\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$4 \mathrm{~N}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$16 \mathrm{~N}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$20 \mathrm{~N}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$22 \mathrm{~N}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$22 \mathrm{~N}$</span> </div>

answer:
<div class="solution">Let the velocity of the ball just when it leaves the hand is $u$ then applying,
<br/> <br/>$\begin{array}{l}
<br/> <br/>v^{2}-u^{2}=2 a \text { for upward journey } \\
<br/> <br/>\Rightarrow-u^{2}=2(-10) \times 2 \\
<br/> <br/>\Rightarrow u^{2}=40
<br/> <br/>\end{array}$
<br/> <br/>Again applying $v^{2}-u^{2}=2 a s$ for the upward journey of the ball, when the ball is in the hands of the thrower,
<br/> <br/>$\begin{array}{l}
<br/> <br/>v^{2}-u^{2}=2 a s \\
<br/> <br/>\Rightarrow 40-0=2(a) 0.2 \\
<br/> <br/>\Rightarrow a=100 \mathrm{~m} / \mathrm{s}^{2} \\
<br/> <br/>\therefore \mathrm{F}=m a=0.2 \times 100=20 \mathrm{~N} \\
<br/> <br/>\Rightarrow \mathrm{N}-m g=20 \\
<br/> <br/>\Rightarrow \mathrm{N}=20+2=22 \mathrm{~N}
<br/> <br/>\end{array}$</div>


slug: a-ball-whose-density-is-0-4-1-0-3-kg-m-3-falls-into-water-from-a-height-of-9-cm-to-what-depth-66942
tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2013']
answer: <div class="solution">No Solution</div>
source_db: MarksBatch0.db
title:
A ball whose density is 0.4 Ã 1 0 3 kg / m 3 falls into water from a height of 9 cm . To what depth does the ball sink?

question:
<div class="question">$\quad$ A ball whose density is $0.4 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ falls into water from a height of $9 \mathrm{~cm}$. To what depth does the ball sink?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 \mathrm{~cm}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$6 \mathrm{~cm}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$4.5 \mathrm{~cm}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2.25 \mathrm{~cm}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$6 \mathrm{~cm}$</span> </div>


slug: a-balloon-is-filled-at-27-c-and-1-atm-pressure-by-500-m-3-he-at-3-c-and-0-5-atm-pressure-96809
tags: ['Physics', 'Kinetic Theory of Gases', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch0.db
title:
A balloon is filled at 27 Â° C and 1 atm pressure by 500 m 3 He . At - 3 Â° C and 0 . 5 atm pressure, the volume of He will be

question:
<div class="question">A balloon is filled at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn><mo> </mo><mo>°</mo><mi mathvariant="normal">C</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi>atm</mi></math> pressure by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mo> </mo><msup><mi mathvariant="normal">m</mi><mn>3</mn></msup></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>He</mi></math>. At <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo> </mo><mo>°</mo><mi mathvariant="normal">C</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>atm</mi></math> pressure, the volume of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>He</mi></math> will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>700</mn><mo> </mo><msup><mi mathvariant="normal">m</mi><mn>3</mn></msup></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>900</mn><mo> </mo><msup><mi mathvariant="normal">m</mi><mn>3</mn></msup></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn><mo> </mo><msup><mi mathvariant="normal">m</mi><mn>3</mn></msup></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mo> </mo><msup><mi mathvariant="normal">m</mi><mn>3</mn></msup></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>900</mn><mo> </mo><msup><mi mathvariant="normal">m</mi><mn>3</mn></msup></math></span> </div>

answer:
<div class="solution"><p>We have, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msub><mi>P</mi><mn>1</mn></msub><msub><mi>V</mi><mn>1</mn></msub></mrow><msub><mi>T</mi><mn>1</mn></msub></mfrac><mo>=</mo><mfrac><mrow><msub><mi>P</mi><mn>2</mn></msub><msub><mi>V</mi><mn>2</mn></msub></mrow><msub><mi>T</mi><mn>2</mn></msub></mfrac></math></p><p>or <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mn>2</mn></msub><mo>=</mo><mfrac><mrow><msub><mi>P</mi><mn>1</mn></msub><msub><mi>V</mi><mn>1</mn></msub><msub><mi>T</mi><mn>2</mn></msub></mrow><mrow><msub><mi>P</mi><mn>2</mn></msub><msub><mi>T</mi><mn>1</mn></msub></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>1</mn><mo>×</mo><mn>500</mn><mo>×</mo><mfenced><mrow><mn>273</mn><mo>-</mo><mn>3</mn></mrow></mfenced></mrow><mrow><mn>0</mn><mo>.</mo><mn>5</mn><mo>×</mo><mfenced><mrow><mn>273</mn><mo>+</mo><mn>27</mn></mrow></mfenced></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mo>×</mo><mn>500</mn><mo>×</mo><mn>270</mn></mrow><mrow><mn>0</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>300</mn></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mn>2</mn></msub><mo>=</mo><mn>900</mn><mo> </mo><msup><mi mathvariant="normal">m</mi><mn>3</mn></msup></math></p></div>


tags: ['Physics', 'Motion In One Dimension', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch0.db
title:
A balloon is rising vertically up with a velocity of 29 ms â 1 . A stone is dropped from it and it reaches the ground in 10 seconds. The height of the balloon when the stone was dropped from it, was ( g = 9.8 ms â 2 )

slug:
a-balloon-is-rising-vertically-up-with-a-velocity-of-29-ms-1-a-stone-is-dropped-from-it-and-it-57092

question:
<div class="question">A balloon is rising vertically up with a velocity of $29 \mathrm{~ms}^{-1}$. A stone is dropped from it and it reaches the ground in 10 seconds. The height of the balloon when the stone was dropped from it, was $\left(\mathrm{g}=9.8 \mathrm{~ms}^{-2}\right)$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$100 \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$200 \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$400 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$150 \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$200 \mathrm{~m}$</span> </div>

answer:
<div class="solution">For stone to be dropped from rising balloon of velocity $29 \mathrm{~m} / \mathrm{s}, \mathrm{u}=-29 \mathrm{~m} / \mathrm{s}, \mathrm{t}=10 \mathrm{sec} .$
<br/> <br/>$\begin{array}{l}
<br/> <br/>\therefore \mathrm{h}=-29 \times 10+\frac{1}{2} \times 9.8 \times 100 \\
<br/> <br/>=-290+490=200 \mathrm{~m} .
<br/> <br/>\end{array}$</div>


tags: ['Physics', 'Ray Optics', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch0.db
title:
A biconvex lens has a radius of curvature of magnitude 20 cm . Which one of the following options best describe the image formed of an object of height 2 cm placed 30 cm from the lens?

slug:
a-biconvex-lens-has-a-radius-of-curvature-of-magnitude-20-cm-which-one-of-the-following-options-be-90740

question:
<div class="question">A biconvex lens has a radius of curvature of magnitude $20 \mathrm{~cm}$. Which one of the following options best describe the image formed of an object of height $2 \mathrm{~cm}$ placed $30 \mathrm{~cm}$ from the lens?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Virtual, upright, height $=1 \mathrm{~cm}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Virtual, upright, height $=0.5 \mathrm{~cm}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Real, inverted, height $=4 \mathrm{~cm}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Real, inverted, height $=1 \mathrm{~cm}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Real, inverted, height $=4 \mathrm{~cm}$</span> </div>

answer:
<div class="solution">In the branch containing \(L\) and \(R_{2}\)
<br/> <br/>\(\begin{aligned} &amp;\mathrm{i}=\frac{\mathrm{E}}{\mathrm{R}_{2}}\left(1-\mathrm{e}^{-\frac{\mathrm{R}_{2} \mathrm{t}}{\mathrm{L}}}\right) \\ &amp;\frac{\mathrm{di}}{\mathrm{dt}}=\frac{\mathrm{E}}{\mathrm{R}_{2}} \mathrm{e}^{-\frac{\mathrm{R}_{2} \mathrm{t}}{\mathrm{L}}} \cdot \frac{\mathrm{R}_{2}}{\mathrm{~L}}=\frac{\mathrm{E}}{\mathrm{L}} \mathrm{e}^{-\frac{\mathrm{R}_{2} \mathrm{t}}{\mathrm{L}}} \\ &amp;\therefore \mathrm{V}_{\mathrm{L}}=\mathrm{L} \frac{\mathrm{di}}{\mathrm{dt}}=\mathrm{Ee}^{-\frac{\mathrm{R}_{2} \mathrm{t}}{\mathrm{L}}} \\ &amp;=12 \mathrm{e}^{-\frac{2 \mathrm{t}}{400 \times 10^{-3}}}=12 \mathrm{e}^{-5 \mathrm{t}} \mathrm{V} \end{aligned}\)</div>


tags: ['Physics', 'Kinetic Theory of Gases', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch0.db
title:
A bicycle tyre is filled with air having pressure of 270 kPa at 2 7 â C . The approximate pressure of the air in the tyre when the temperature increases to 3 6 â C is

slug:
a-bicycle-tyre-is-filled-with-air-having-pressure-of-270-kpa-at-2-7-c-the-approximate-pressure-38219

question:
<div class="question">A bicycle tyre is filled with air having pressure of $270 \mathrm{kPa}$ at $27^{\circ} \mathrm{C}$. The approximate pressure of the air in the tyre when the temperature increases to $36^{\circ} \mathrm{C}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$270 \mathrm{kPa}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$262 \mathrm{KPa}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$278 \mathrm{kPa}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$360 \mathrm{kPa}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$278 \mathrm{kPa}$</span> </div>

answer:
<div class="solution">From the ideal gas equation $\mathrm{PV}=\mathrm{nRT}$ Here, volume is constant $\therefore \frac{\mathrm{P}_1}{\mathrm{~T}_1}=\frac{\mathrm{P}_2}{\mathrm{~T}_2}$<br/>Here, $T_1=27+273=300 \mathrm{~K}$<br/>$P_1=270 \mathrm{kPa}$<br/>$\mathrm{T}_2=36+273=309 \mathrm{~K}$<br/>$\Rightarrow P_2=\frac{P_1}{T_1} \times T_2=\frac{270 \times(309)}{300}=278 \mathrm{kPa}$</div>


tags: ['Mathematics', 'Functions', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch0.db
title:
A black die and a white die are rolled. Find the probability that the number shown by the black die will be more than twice that shown by the white die.

slug:
a-black-die-and-a-white-die-are-rolled-find-the-probability-that-the-number-shown-by-the-black-die-79674

question:
<div class="question">A black die and a white die are rolled. Find the probability that the number shown by the black die will be more than twice that shown by the white die.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(1 / 8\)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\(1 / 6\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(1 / 3\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(1 / 4\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(1 / 6\)</span> </div>

answer:
<div class="solution">The number of favourable cases are shown below:<br/>\(\begin{array}{cl}\text { Number on white die } &amp; \text { Number on black die } \\ 1 &amp; 3 \\ 1 &amp; 4 \\ 1 &amp; 5 \\ 1 &amp; 6 \\ 2 &amp; 5 \\ 2 &amp; 6\end{array}\)<br/>There are 6 favourable cases in which the number on black die is more than twice the number on the white die.<br/>\(\begin{aligned}<br/>&amp; \therefore \mathrm{m}=6 \\<br/>&amp; \mathrm{n}=\text { Total number of cases }=6 \times 6<br/>\end{aligned}\)<br/>( \(\therefore\) with each die there are six possibilities)<br/>\(\therefore\) Probability \(\mathrm{p}=\frac{\mathrm{m}}{\mathrm{n}}=\frac{6}{6 \times 6}=\frac{1}{6}\)</div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch0.db
title:
A block A of mass 100 kg rests on another block B of mass 200 kg and is tied to a wall as shown in the figure. The coefficient of friction between A and B is 0 . 2 and that between B and ground is 0 . 3 . The minimum force required to move the block B is g = 10 m s - 2

slug:
a-block-a-of-mass-100-kg-rests-on-another-block-b-of-mass-200-kg-and-is-tied-to-a-wall-as-shown-in-t-61143

question:
<div class="question"><p>A block <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> of mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo> </mo><mi>kg</mi></math> rests on another block <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> of mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn><mo> </mo><mi>kg</mi></math> and is tied to a wall as shown in the figure. The coefficient of friction between <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>2</mn></math> and that between <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> and ground is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>3</mn></math>. The minimum force required to move the block <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>g</mi><mo>=</mo><mn>10</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></mrow></mfenced></math></p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/20b64890-e2fb-4605-8f23-17f02bacd887-image.png" style="width: 300px; height: 129px;"/></p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>900</mn><mo> </mo><mi mathvariant="normal">N</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn><mo> </mo><mi mathvariant="normal">N</mi></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1100</mn><mo> </mo><mi mathvariant="normal">N</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>700</mn><mo> </mo><mi mathvariant="normal">N</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1100</mn><mo> </mo><mi mathvariant="normal">N</mi></math></span> </div>

answer:
<div class="solution"><p>Friction force between <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> and between block <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> and surface <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math> will oppose <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mi>F</mi><mo>=</mo><msub><mi>F</mi><mrow><mi>A</mi><mi>B</mi></mrow></msub><mo>+</mo><msub><mi>F</mi><mrow><mi>B</mi><mi>S</mi></mrow></msub><mo>=</mo><msub><mi>μ</mi><mrow><mi>A</mi><mi>B</mi></mrow></msub><msub><mi>M</mi><mi>A</mi></msub><mi>g</mi><mo>+</mo><msub><mi>μ</mi><mrow><mi>B</mi><mi>S</mi></mrow></msub><mfenced><mrow><msub><mi>m</mi><mi>A</mi></msub><mo>+</mo><msub><mi>m</mi><mi>B</mi></msub></mrow></mfenced><mi>g</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn><mo>×</mo><mn>100</mn><mo>×</mo><mn>10</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>3</mn><mfenced><mrow><mn>100</mn><mo>+</mo><mn>200</mn></mrow></mfenced><mo>×</mo><mn>10</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>200</mn><mo>+</mo><mn>900</mn><mo>=</mo><mn>1100</mn><mo> </mo><mi mathvariant="normal">N</mi></math></p></div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch0.db
title:
A block of mass m is placed on a smooth inclined wedge A BC of inclination Î¸ as shown in the figure. The wedge is given an acceleration 'a' towards the right. The relation between a and Î¸ for the block to remain stationary on the wedge is

slug:
a-block-of-mass-m-is-placed-on-a-smooth-inclined-wedge-a-bc-of-inclination-as-shown-in-the-figure-43954

question:
<div class="question">A block of mass m is placed on a smooth inclined wedge $A B C$ of inclination $\theta$ as shown in the figure. The wedge is given an acceleration 'a' towards the right. The relation between a and $\theta$ for the block to remain stationary on the wedge is
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/6elWAXz6q9osdRlGR5hP02iRBVuwHR0J8DkFfiRalJA.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$a=\frac{g}{\operatorname{cosec} \theta}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$a=\frac{g}{\sin \theta}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$a=g \tan \theta$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$a=g \cos \theta$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$a=g \tan \theta$</span> </div>

answer:
<div class="solution">Let the mass of block is m. It will remains stationary if forces acting on it are in equilibrium. i.e., $m a \cos \theta=m g \sin \theta$
<br/> <br/>$\Rightarrow a=g \tan \theta$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/6Kt7aR7rSEsAgzZdB-12ihl9_xlN6SnNnJoueun6tjg.original.fullsize.png"/><br/> <br/> <br/>Here $\mathrm{ma}=$ Pseudo force on block,
<br/> <br/>$\mathrm{mg}=$ weight</div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2009']
answer: <div class="solution">No Solution available</div>
source_db: MarksBatch0.db
title:
A block of mass M is pulled along a horizontal frictionless surface by a rope of mass M /2 . If a force 2 Mg is applied at one end of the rope, the force which the rope exerts on the block is -

slug:
a-block-of-mass-m-is-pulled-along-a-horizontal-frictionless-surface-by-a-rope-of-mass-m-2-if-a-fo-49607

question:
<div class="question">A block of mass $\mathrm{M}$ is pulled along a horizontal frictionless surface by a rope of mass $\mathrm{M} / 2$. If a force $2 \mathrm{Mg}$ is applied at one end of the rope, the force which the rope exerts on the block is -</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 \mathrm{Mg} / 3$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 \mathrm{Mg}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$4 \mathrm{Mg} / 3$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">zero</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$4 \mathrm{Mg} / 3$</span> </div>


slug: a-block-of-wood-floats-in-water-with-4-5-th-of-its-volume-submerged-if-the-same-block-just-fl-26788
tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch0.db
title:
A block of wood floats in water with ( 4 / 5 ) th of its volume submerged. If the same block just floate in a liquid, the density of liquid in kg m - 3 is

question:
<div class="question">A block of wood floats in water with <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>4</mn><mo>/</mo><mn>5</mn><msup><mo>)</mo><mi>th</mi></msup></math> of its volume submerged. If the same block just floate in a liquid, the density of liquid in <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>kg</mi><mo> </mo><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow></mfenced></math> is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1250</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>600</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>400</mn></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>800</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>800</mn></math></span> </div>

answer:
<div class="solution"><p>Let <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi></math> be the volume of the block. When block floats in water, then <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mrow><mi>block</mi><mo> </mo></mrow></msub><mi>g</mi><mo>=</mo><mfenced><mrow><mfrac><mn>4</mn><mn>5</mn></mfrac><mi>v</mi></mrow></mfenced><msub><mi>ρ</mi><mrow><mi>water</mi><mo> </mo></mrow></msub><mi>g</mi></math></p><p>or <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mi>block</mi></msub><mo>=</mo><mfrac><mn>4</mn><mn>5</mn></mfrac><msub><mi>ρ</mi><mrow><mi>water</mi><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo></mrow></msub><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mi mathvariant="normal">i</mi></mfenced></math></p><p>When block floats in liquid.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><msub><mi>ρ</mi><mrow><mi>block</mi><mo> </mo></mrow></msub><mi>g</mi><mo>=</mo><mi>V</mi><msub><mi>ρ</mi><mi>liquid</mi></msub><mi>g</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ρ</mi><mrow><mi>block</mi><mo> </mo></mrow></msub><mo>=</mo><msub><mi>ρ</mi><mrow><mi>liquid</mi><mo> </mo></mrow></msub></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ρ</mi><mrow><mi>liquid</mi><mo> </mo></mrow></msub><mo>=</mo><mfrac><mn>4</mn><mn>5</mn></mfrac><msub><mi>ρ</mi><mrow><mi>water</mi><mo> </mo></mrow></msub></math> [from Eq. (i)]</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>4</mn><mn>5</mn></mfrac><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo> </mo><mi>kg</mi><mo> </mo><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>800</mn><mo> </mo><mi>kg</mi><mo> </mo><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></math></p></div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch0.db
title:
A bob is hanging over a pulley inside a car through, a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration 'a' directed horizontallyas shown in figure. Other end of the string is pulled with constant acceleration 'a' vertically. The tension in the string is equal to -

slug:
a-bob-is-hanging-over-a-pulley-inside-a-car-through-a-string-the-second-end-of-the-string-is-in-th-55790

question:
<div class="question">A bob is hanging over a pulley inside a car through, a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration 'a' directed horizontallyas shown in figure. Other end of the string is pulled with constant acceleration 'a' vertically. The tension in the string is equal to -
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/MeCzqZkN_4t-0bPL-U9GAfikCf7uFvQ2jL2VZc9tzKw.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$m \sqrt{g^{2}+a^{2}}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$m \sqrt{g^{2}+a^{2}}-m a$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{m} \sqrt{\mathrm{g}^{2}+\mathrm{a}^{2}}+\mathrm{ma}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{m}(\mathrm{g}+\mathrm{a})$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{m} \sqrt{\mathrm{g}^{2}+\mathrm{a}^{2}}+\mathrm{ma}$</span> </div>

answer:
<div class="solution">Applying Newton's law
<br/> <br/>along string
<br/> <br/>$$
<br/> <br/>\Rightarrow \mathrm{T}-\mathrm{m} \sqrt{\mathrm{g}^{2}+\mathrm{a}^{2}}=\mathrm{ma}
<br/> <br/>$$
<br/> <br/>or $\mathrm{T}=\mathrm{m} \sqrt{\mathrm{g}^{2}+\mathrm{a}^{2}}+\mathrm{ma}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/LkCzNOWXg3KqhyEpoBFRL0Q4wHXBJ8DHCj7AxaIoNk8.original.fullsize.png"/></div>


tags: ['Physics', 'Work Power Energy', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch0.db
title:
A body is moving unidirectionally under the influence of a source of constant power. The square of its displacement in time t is proportional to

slug:
a-body-is-moving-unidirectionally-under-the-influence-of-a-source-of-constant-power-the-square-of-i-51968

question:
<div class="question">A body is moving unidirectionally under the influence of a source of constant power. The square of its displacement in time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> is proportional to</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>t</mi><mn>3</mn></msup></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>t</mi><mn>2</mn></msup></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mi>t</mi></msqrt></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>t</mi><mn>3</mn></msup></math></span> </div>

answer:
<div class="solution"><p>By work-energy theorem,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>W</mi><mo>=</mo><mi>P</mi><mo>×</mo><mi>t</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msup><mi>v</mi><mn>2</mn></msup><mo>=</mo><mn>2</mn><mfrac><mrow><mi>P</mi><mi>t</mi></mrow><mi>m</mi></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><msup><mfenced><mfrac><mrow><mn>2</mn><mi>P</mi><mi>t</mi></mrow><mi>m</mi></mfrac></mfenced><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math></p><p>or <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>d</mi><mi>s</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><msup><mfenced><mfrac><mrow><mn>2</mn><mi>P</mi><mi>t</mi></mrow><mi>m</mi></mfrac></mfenced><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∫</mo><mi>d</mi><mi>s</mi><mo>=</mo><mo>∫</mo><msup><mfenced><mfrac><mrow><mn>2</mn><mi>P</mi><mi>t</mi></mrow><mi>m</mi></mfrac></mfenced><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mi>d</mi><mi>t</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msup><mfenced><mfrac><mrow><mn>2</mn><mi>P</mi></mrow><mi>m</mi></mfrac></mfenced><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>·</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><msup><mi>t</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup></math></p><p>i.e. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>∝</mo><msup><mi>t</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>s</mi><mn>2</mn></msup><mo>∝</mo><msup><mi>t</mi><mn>3</mn></msup></math></p></div>


tags: ['Physics', 'Motion In Two Dimensions', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch0.db
title:
A body is projected, making an acute angle with the horizontal. If angle between velocity v and acceleration g â is Î¸ , then

slug:
a-body-is-projected-making-an-acute-angle-with-the-horizontal-if-angle-between-velocity-v-and-acce-76747

question:
<div class="question">A body is projected, making an acute angle with the horizontal. If angle between velocity $\vec{v}$ and acceleration $\overrightarrow{\mathrm{g}}$ is $\theta,$ then</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\theta=90^{\circ}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\quad \theta=0^{\circ}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$90^{\circ}&lt;\theta&lt;0^{\circ}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$0^{\circ}&lt;\theta&lt;180^{\circ}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0^{\circ}&lt;\theta&lt;180^{\circ}$</span> </div>

answer:
<div class="solution">Here velocity is acting upwards when projectile is going upwards and acceleration is downwards. The angle $\theta$ between $\overrightarrow{\mathrm{v}}$ and $\overrightarrow{\text { a }}$ is more than $0^{\circ}$ and less than $180^{\circ}$</div>


tags: ['Physics', 'Motion In One Dimension', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch0.db
title:
A body is thrown vertically upwards from A, the top of the tower, reaches the ground in time t 1 â . If it is thrown vertically downwards from A with the same speed, it reaches the ground in time t 2 â . If it is allowed to fall freely from A , then the time it takes to reach the ground is given by

slug:
a-body-is-thrown-vertically-upwards-from-a-the-top-of-the-tower-reaches-the-ground-in-time-t-1-52927

question:
<div class="question">A body is thrown vertically upwards from A, the top of the tower, reaches the ground in time $t_{1}$. If it is thrown vertically downwards from A with the same speed, it reaches the ground in time $\mathrm{t}_{2}$. If it is allowed to fall freely from $\mathrm{A},$ then the time it takes to reach the ground is given by</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{t}=\frac{\mathrm{t}_{1}+\mathrm{t}_{2}}{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{t}=\frac{\mathrm{t}_{1}-\mathrm{t}_{2}}{2}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\quad \mathrm{t}=\sqrt{\mathrm{t}_{1} \mathrm{t}_{2}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{t}=\sqrt{\frac{\mathrm{t}_{1}}{\mathrm{t}_{2}}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\quad \mathrm{t}=\sqrt{\mathrm{t}_{1} \mathrm{t}_{2}}$</span> </div>

answer:
<div class="solution">Let the body is projected vertically upwards from A with a speed $u_{0}$ Using equation, $\mathrm{s}=\mathrm{ut}+\frac{1}{2} \mathrm{at}^{2}$
<br/> <br/>For case $(1)-\mathrm{h}=\mathrm{u}_{0} \mathrm{t}_{1}-\frac{1}{2} \mathrm{gt}_{1}^{2} \quad \ldots(1)$
<br/> <br/>For case (2) $-\mathrm{h}=\mathrm{u}_{0} \mathrm{t}_{2}-\frac{1}{2} \mathrm{gt}_{1}^{2}$
<br/> <br/>Subtracting eq (2) from (1), we get
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>0=\mathrm{u}_{0}\left(\mathrm{t}_{2}+\mathrm{t}_{1}\right)+\frac{1}{2} \mathrm{~g}\left(\mathrm{t}_{2}^{2}-\mathrm{t}_{1}^{2}\right) \\
<br/> <br/>\Rightarrow \mathrm{u}_{0}=\frac{1}{2} \mathrm{~g}\left(\mathrm{t}_{1}-\mathrm{t}_{2}\right)
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>Putting the value of $\mathrm{u}_{0}$ in eq (2), we get
<br/> <br/>$$
<br/> <br/>-\mathrm{h}=-\left(\frac{1}{2}\right) \mathrm{g}\left(\mathrm{t}_{1}-\mathrm{t}_{2}\right) \mathrm{t}_{2}-\left(\frac{1}{2}\right) \mathrm{gt}_{2}^{2}
<br/> <br/>$$
<br/> <br/>$$
<br/> <br/>\Rightarrow \mathrm{h}=\frac{1}{2} \mathrm{~g}\left(\mathrm{t}_{1} \mathrm{t}_{2}\right)
<br/> <br/>$$
<br/> <br/>For case $3, \mathrm{u}_{0}=0, \mathrm{t}=?$
<br/> <br/>$$
<br/> <br/>-\mathrm{h}=0 \times \mathrm{t}-\left(\frac{1}{2}\right) \mathrm{gt}^{2}
<br/> <br/>$$
<br/> <br/>$\mathrm{h}=\left(\frac{1}{2}\right) \mathrm{gt}^{2}$
<br/> <br/>Comparing eq. (4) and $(5),$ we get
<br/> <br/>$$
<br/> <br/>\frac{1}{2} \mathrm{gt}^{2}=\frac{1}{2} \mathrm{gt}_{1} \mathrm{t}_{2} \quad \therefore \mathrm{t}=\sqrt{\mathrm{t}_{1} \mathrm{t}_{2}}
<br/> <br/>$$</div>


title: A body is travelling in a circle at a constant speed. It
slug: a-body-is-travelling-in-a-circle-at-a-constant-speed-it-47026
question: <div class="question">A body is travelling in a circle at a constant speed. It</div>
tags: ['Physics', 'Motion In Two Dimensions', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch0.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">has a constant velocity</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">is not accelerated</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">has an inward radial acceleration</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">has an outward radial acceleration</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">has an inward radial acceleration</span> </div>

answer:
<div class="solution">Body moves with constant speed it means that tangential acceleration $\mathrm{a}_{\mathrm{T}}=0 \&amp; \mathrm{conly}$ centripetal acceleration $\mathrm{a}_{\mathrm{C}}$ exists whose direction is always towards the centre or inward (along the radius of the circle).</div>


title: A body moves with uniform acceleration, then which of the following graph is correct?
slug: a-body-moves-with-uniform-acceleration-then-which-of-the-following-graph-is-correct-69641
tags: ['Physics', 'Motion In One Dimension', 'JEE Main']
source_db: MarksBatch0.db
question:
<div class="question">A body moves with uniform acceleration, then which of the following graph is correct?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/qR6bhfrifCO0s7hleCQyLX-wbA8lqA3SIcJ9NWIuqxg.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/sH0QxPXPNGB7GOMynNN8UeUEzh2MbN1_cKePGzVuwQw.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ImoGN37Q8Fucfa1wETFiFFnSkDVmgW9ytAax5dTXZBY.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/CwDT_PyhEyQZ2YxMZ2VLWEVqSaAB5t-omR-d6SmMfU8.original.fullsize.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ImoGN37Q8Fucfa1wETFiFFnSkDVmgW9ytAax5dTXZBY.original.fullsize.png"/></span> </div>

answer:
<div class="solution">An object is said to be moving with a uniform acceleration, if its velocity changes by equal amount in equal intervals of time. The velocity-time graph of uniformly accelerated motion is a straight line inclined to time axis. Acceleration of an object in a uniformly accelerated motion in one dimension is equal to the slope of the velocity-time graph with time axis.</div>


slug: a-body-of-density-is-dropped-from-rest-at-a-height-h-into-a-lake-of-density-where-80813
tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch0.db
title:
A body of density Ï â² is dropped from rest at a height h into a lake of density Ï where Ï > Ï â² neglecting all dissipative forces, calculate the maximum depth to which the body sinks before returning to float on the surface:

question:
<div class="question">A body of density $\rho^{\prime}$ is dropped from rest at a height h into a lake of density $\rho$ where $\rho&gt;\rho^{\prime}$ neglecting all dissipative forces, calculate the maximum depth to which the body sinks before returning to float on the surface:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\mathrm{h}}{\rho-\rho^{\prime}}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\mathrm{h} \rho^{\prime}}{\rho}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{\mathrm{h} \rho^{\prime}}{\rho-\rho^{\prime}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{h \rho}{\rho-\rho^{\prime}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{h} \rho^{\prime}}{\rho-\rho^{\prime}}$</span> </div>

answer:
<div class="solution">The effective acceleration of the body
<br/> <br/>$\mathrm{g}^{\prime}=\left(1-\frac{\rho}{\rho^{\prime}}\right) \mathrm{g}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/oEm_LCHuM0OzQE1UaLX4fufNHlvQQinJ9ebj1CpNf08.original.fullsize.png"/><br/> <br/> <br/>Now, the depth to which the body sinks
<br/> <br/>$\mathrm{h}^{\prime}=\left(\frac{\mathrm{u}^{2}}{2 \mathrm{~g}^{\prime}}\right)=\frac{2 \mathrm{gh}}{2 \mathrm{~g}^{\prime}}=\frac{\mathrm{gh}}{\mathrm{g}^{\prime}}=\frac{\mathrm{h} \times \rho^{\prime}}{\rho-\rho^{\prime}}$</div>


tags: ['Physics', 'Thermal Properties of Matter', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch0.db
title:
A body of length 1 m having cross-sectional area 0.75 m 2 has heat flow through it at the rate of 6000 Joule/sec. Then find the temperature difference if K = 200 Jm â 1 K â 1

slug:
a-body-of-length-1-m-having-cross-sectional-area-0-75-m-2-has-heat-flow-through-it-at-the-rate-of-60-73292

question:
<div class="question">A body of length $1 \mathrm{~m}$ having cross-sectional area $0.75 \mathrm{~m}^{2}$ has heat flow through it at the rate of 6000 Joule/sec. Then find the temperature difference if $\mathrm{K}=200 \mathrm{Jm}^{-1} \mathrm{~K}^{-1}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$20^{\circ} \mathrm{C}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$40^{\circ} \mathrm{C}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$80^{\circ} \mathrm{C}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$100^{\circ} \mathrm{C}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$40^{\circ} \mathrm{C}$</span> </div>

answer:
<div class="solution">$\frac{Q}{t}=\frac{\operatorname{KA} \Delta \theta}{\ell} \Rightarrow 6000=\frac{200 \times 0.75 \times \Delta \theta}{1}$<br/>$\therefore \Delta \theta=\frac{6000 \times 1}{200 \times 0.75}=40^{\circ} \mathrm{C}$</div>


tags: ['Physics', 'Oscillations', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch0.db
title:
A body of mass 1 kg is executing simple harmonic motion. Its displacement y cm at t seconds is given by y = 6 sin 100 t + Ï 4 . Its maximum kinetic energy is

slug:
a-body-of-mass-1-kg-is-executing-simple-harmonic-motion-its-displacement-y-cm-at-t-seconds-is-given-36881

question:
<div class="question"><p>A body of mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi>kg</mi></math> is executing simple harmonic motion. Its displacement <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mfenced><mi>cm</mi></mfenced></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> seconds is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>6</mn><mi>sin</mi><mfenced><mrow><mn>100</mn><mi>t</mi><mo>+</mo><mfrac><mi>π</mi><mn>4</mn></mfrac></mrow></mfenced></math>. Its maximum kinetic energy is</p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo> </mo><mi mathvariant="normal">J</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo> </mo><mi mathvariant="normal">J</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn><mo> </mo><mi mathvariant="normal">J</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn><mo> </mo><mi mathvariant="normal">J</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo> </mo><mi mathvariant="normal">J</mi></math></span> </div>

answer:
<div class="solution"><p>Given, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>6</mn><mo> </mo><mi>cm</mi><mo>=</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo> </mo><mi mathvariant="normal">m</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">ω</mi><mo>=</mo><mn>100</mn><mo> </mo><mi>rad</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>,</mo><mi mathvariant="normal">m</mi><mo>=</mo><mn>1</mn><mo> </mo><mi>kg</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>K</mi><mi>max</mi></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>m</mi><msup><mi>ω</mi><mn>2</mn></msup><msup><mi>a</mi><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>1</mn><mo>×</mo><msup><mfenced><mn>100</mn></mfenced><mn>2</mn></msup><mo>×</mo><msup><mfenced><mrow><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup></mrow></mfenced><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>18</mn><mo> </mo><mi mathvariant="normal">J</mi></math></p></div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch0.db
title:
A body of mass 2 kg is placed on a horizontal surface having kinetic friction 0.4 and static friction 0.5. If the force applied on the body is 2.5 N , then the frictional force acting on the body will be [ g = 10 ms â 2 ]

slug:
a-body-of-mass-2-kg-is-placed-on-a-horizontal-surface-having-kinetic-friction-0-4-and-static-frictio-53998

question:
<div class="question">A body of mass $2 \mathrm{~kg}$ is placed on a horizontal surface having kinetic friction 0.4 and static friction $0.5 .$ If the force applied on the body is $2.5 \mathrm{~N},$ then the frictional force acting on the body will be $\left[\mathrm{g}=10 \mathrm{~ms}^{-2}\right]$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$8 \mathrm{~N}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$10 \mathrm{~N}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$20 \mathrm{~N}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$2.5 \mathrm{~N}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2.5 \mathrm{~N}$</span> </div>

answer:
<div class="solution">Limiting friction $=0.5 \times 2 \times 10=10 \mathrm{~N}$
<br/> <br/>The applied force is less than force of friction, therefore the force of friction is equal to the applied force.</div>


slug: a-body-of-mass-m-is-moving-in-a-straight-line-with-momentum-p-starting-at-time-t-0-a-force-f-47593
tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch0.db
title:
A body of mass m is moving in a straight line with momentum p . Starting at time t = 0 , a force F = a t acts in the same direction on the moving particle during time interval of T . So that its momentum changes from p to 2 p . The value of T is

question:
<div class="question">A body of mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> is moving in a straight line with momentum <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math>. Starting at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math>, a force <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mi>a</mi><mi>t</mi></math> acts in the same direction on the moving particle during time interval of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>. So that its momentum changes from <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>p</mi></math>. The value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math> is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>2</mn><mi>p</mi></mrow><mi>a</mi></mfrac></msqrt></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mi>p</mi><mi>a</mi></mfrac></msqrt></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msqrt><mfrac><mrow><mn>2</mn><mi>p</mi></mrow><mi>a</mi></mfrac></msqrt></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi>p</mi></mrow><mi>a</mi></mfrac></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mrow><mn>2</mn><mi>p</mi></mrow><mi>a</mi></mfrac></msqrt></math></span> </div>

answer:
<div class="solution"><p>Given, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mi>a</mi><mi>t</mi></math></p><p>when, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn></math>, then linear momentum <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>p</mi></math></p><p>when, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>T</mi></math>, then linear momentum <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mi>p</mi></math></p><p>According to Newton's law of motion, applied force, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfrac><mrow><mi>d</mi><mi>p</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></math></p><p>or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>p</mi><mo>=</mo><mi>F</mi><mi>d</mi><mi>t</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi>p</mi><mo>=</mo><mi>a</mi><mi>t</mi><mi>d</mi><mi>t</mi></math></p><p>or <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mo>∫</mo><mi>p</mi><mrow><mn>2</mn><mi>p</mi></mrow></msubsup><mi>d</mi><mi>p</mi><mo>=</mo><mi>a</mi><msubsup><mo>∫</mo><mn>0</mn><mi>T</mi></msubsup><mi>t</mi><mi>d</mi><mi>t</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>2</mn><mi>p</mi><mo>-</mo><mi>p</mi></mrow></mfenced><mo>=</mo><mi>a</mi><mo>·</mo><mfrac><msup><mi>T</mi><mn>2</mn></msup><mn>2</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mrow><mn>2</mn><mi>p</mi></mrow><mi>a</mi></mfrac><mo>=</mo><msup><mi>T</mi><mn>2</mn></msup><mo>⇒</mo><mi>T</mi><mo>=</mo><msqrt><mfrac><mrow><mn>2</mn><mi>p</mi></mrow><mi>a</mi></mfrac></msqrt></math></p></div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch0.db
title:
A body of weight 2 kg is suspended as shown in the figure. The tension T 1 â in the horizontal string (in kg wt ) is

slug:
a-body-of-weight-2-kg-is-suspended-as-shown-in-the-figure-the-tension-t-1-in-the-horizontal-str-35745

question:
<div class="question">A body of weight $2 \mathrm{~kg}$ is suspended as shown in the figure. The tension $\mathrm{T}_{1}$ in the horizontal string (in $\mathrm{kg}$ wt ) is
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/M1AX_eSftPIY0bQ28YXsaE8NAl_9yaLTo_jffdjtHu4.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{2}{\sqrt{3}}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\sqrt{3}}{2}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$2 \sqrt{3}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2 \sqrt{3}$</span> </div>

answer:
<div class="solution">The tension in the above string can be divided into two components where the component opposite to weight will balance the weight while the component of this tension opposite to \(\mathrm{T}_{1}\) will be equal to \(\mathrm{T}_{1}\).
<br/> <br/>\(\mathrm{T} \sin \theta=2 \mathrm{~kg} \mathrm{wt}\)
<br/> <br/>\(\mathrm{T} \cos \theta=\mathrm{T}_{1}\)
<br/> <br/>The first equation gives
<br/> <br/>\(\mathrm{T}=4 \mathrm{~kg} \mathrm{wt}\)
<br/> <br/>So \(\mathrm{T}_{1}\) will be,
<br/> <br/>\(\mathrm{T}_{1}=2 \sqrt{3} \mathrm{~kg} \mathrm{wt}\)</div>


title: A Ï bonded molecule MX 3 â is T-shaped. The number of non bonded pair of electrons is
slug: a-bonded-molecule-mx-3-is-t-shaped-the-number-of-non-bonded-pair-of-electrons-is-48851
tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'BITSAT', 'BITSAT 2011']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch0.db
question:
<div class="question">$\mathrm{A} \sigma$ bonded molecule $\mathrm{MX}_{3}$ is T-shaped. The number of non bonded pair of electrons is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">2</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">1</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">can be predicted only if atomic number is known</span> </li> </ul>

answer:
<div class="solution">For T-shape geometry the molecule must have 3 bonded pair and 2 lone pair of electrons.</div>


slug: a-bowl-filled-with-very-hot-soup-cools-from-9-8-c-to-8-6-c-in-2-minutes-when-the-room-temper-80459
tags: ['Physics', 'Thermal Properties of Matter', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch0.db
title:
A bowl filled with very hot soup cools from 9 8 â C to 8 6 â C in 2 minutes when the room temperature is 2 2 â C . How long it will take to cool from 7 5 â C to 6 9 â C ?

question:
<div class="question">A bowl filled with very hot soup cools from $98^{\circ} \mathrm{C}$ to $86^{\circ} \mathrm{C}$ in 2 minutes when the room temperature is $22^{\circ} \mathrm{C}$. How long it will take to cool from $75^{\circ} \mathrm{C}$ to $69^{\circ} \mathrm{C}$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>2 minutes</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>1.4 minutes</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>0.5 minute</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>1 minute</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>1.4 minutes</span> </div>

answer:
<div class="solution">The rate of heat flow is given by<br/>$\begin{aligned}<br/>&amp; \frac{\Delta Q}{\Delta t}=-K\left(T-T_0\right) \Rightarrow \frac{\Delta Q}{\Delta t}=-K\left(T_{a v g}-T_0\right) \\<br/>&amp; \text { Initially } T_{a v g}=\frac{T_1+T_2}{2} \\<br/>&amp; \text { Here, } T_1=98^{\circ} \mathrm{C} \\<br/>&amp; T_2=86^{\circ} \mathrm{C}<br/>\end{aligned}$<br/>$\begin{aligned} &amp; \text { (i) } \frac{\mathrm{ms} \times 12}{2}=-\mathrm{K}\left(\frac{98+86}{2}-22\right) \\ &amp; 6=-\frac{\mathrm{K}}{\mathrm{ms}}\left[\frac{98+86}{2}-22\right] \quad(\because \Delta \mathrm{Q}=\mathrm{ms} \Delta \mathrm{T})\end{aligned}$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/m-qxoSp3pUGTs9hNmklcIiM0y5wsfF4lw7tCcyRjGXc.original.fullsize.png"/><br/><br/>Now, cool from $\mathrm{T}_1^{\prime}=75^{\circ} \mathrm{C}$<br/>$\begin{aligned}<br/>&amp; \mathrm{T}_2=69^{\circ} \mathrm{C} \\<br/>&amp; \mathrm{T}_{\mathrm{avg}}=\frac{\mathrm{T}_1^{\prime}+\mathrm{T}_2^{\prime}}{2}=\frac{75+69}{2}<br/>\end{aligned}$<br/>(ii) $\frac{\mathrm{ms} \times 6}{\Delta \mathrm{t}}=-\mathrm{K}\left(\frac{75+69}{2}-22\right)$<img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/bQrJV0HZxZIN7yecVk6HwfeL4MYFknI9xPA7NGCSfTw.original.fullsize.png"/><br/><br/>Divide equation (ii) by (i), we have<br/>$\begin{aligned}<br/>&amp; \frac{6}{\Delta t(6)}=\frac{50}{70} \\<br/>&amp; \Delta t=\frac{7}{5}=1.4 \mathrm{~min}<br/>\end{aligned}$</div>


tags: ['Mathematics', 'Permutation Combination', 'BITSAT', 'BITSAT 2013']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">64</span> </div>
source_db: MarksBatch0.db
title:
A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?

slug:
a-box-contains-two-white-balls-three-black-balls-and-four-red-balls-in-how-many-ways-can-three-bal-75404

question:
<div class="question">A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">64</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">129</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">84</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

answer:
<div class="solution">Atleast one black ball can be drawn in the following ways
<br/> <br/>(1) one black and two other colour balls
<br/> <br/>$$
<br/> <br/>={ }^{3} \mathrm{C}_{1} \times{ }^{6} \mathrm{C}_{2}=3 \times 15=45
<br/> <br/>$$
<br/> <br/>(ii) two black and one other colour balls
<br/> <br/>$$
<br/> <br/>={ }^{3} \mathrm{C}_{2} \times{ }^{6} \mathrm{C}_{1}=3 \times 6=18
<br/> <br/>$$
<br/> <br/>(iii) All the three are black $={ }^{3} \mathrm{C}_{3} \times{ }^{6} \mathrm{C}_{0}=1$
<br/> <br/>$\therefore$ Req. no. of ways $=45+18+1=64$</div>


tags: ['Mathematics', 'Probability', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch0.db
title:
A boy is throwing stones at a target. The probability of hitting the target at any trial is 2 1 â The probability of hitting the target 5 th time at the 10 th throw is:

slug:
a-boy-is-throwing-stones-at-a-target-the-probability-of-hitting-the-target-at-any-trial-is-2-1-39455

question:
<div class="question">A boy is throwing stones at a target. The probability of hitting the target at any trial is $\frac{1}{2}$ The probability of hitting the target 5 th time at the 10 th throw is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{5}{2^{10}}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{63}{2^{9}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{10}{2^{10}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{63}{2^{9}}$</span> </div>

answer:
<div class="solution">The probability of hitting the target 5 th time at the 10 th throw $=\mathrm{P}($ the probability of hitting the target 4 times in the first 9 throws) $\mathrm{P}($ the probability of hitting the target at the 10 th throw $)=$
<br/>$\left[{ }^{9} \mathrm{C}_{4}\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{5}\right]\left(\frac{1}{2}\right)=\frac{9 !}{4 ! 5 !} \times\left(\frac{1}{2}\right)^{10}=\frac{63}{2^{9}}$</div>


tags: ['Physics', 'Work Power Energy', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch0.db
title:
A boy pushes a toy box 2.0 m along the floor by means of a force of 10 N directed downward at an angle of 6 0 â to the horizontal. The work done by the boy is

slug:
a-boy-pushes-a-toy-box-2-0-m-along-the-floor-by-means-of-a-force-of-10-n-directed-downward-at-an-ang-86047

question:
<div class="question">A boy pushes a toy box $2.0 \mathrm{~m}$ along the floor by means of a force of $10 \mathrm{~N}$ directed downward at an angle of $60^{\circ}$ to the horizontal. The work done by the boy is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$6 \mathrm{~J}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$8 \mathrm{~J}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$10 \mathrm{~J}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$12 \mathrm{~J}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$10 \mathrm{~J}$</span> </div>

answer:
<div class="solution">$\mathrm{W}=\mathrm{F} \mathrm{s} \cos \theta=10 \times 2 \cos 60^{\circ}=10 \mathrm{~J}$</div>


tags: ['Physics', 'Capacitance', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch0.db
title:
A capacitor of capacitance C is charged to a potential V. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is:

slug:
a-capacitor-of-capacitance-c-is-charged-to-a-potential-v-the-flux-of-the-electric-field-through-a-c-10965

question:
<div class="question">A capacitor of capacitance $C$ is charged to a potential V. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{C V}{2 \varepsilon_0}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{2 \mathrm{CV}}{\varepsilon_0}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{\mathrm{CV}}{\varepsilon_0}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Zero</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{CV}}{\varepsilon_0}$</span> </div>

answer:
<div class="solution">From the Gauss's law<br/>$\begin{aligned}<br/>&amp; \phi=\frac{\mathrm{q}_{\text {in }}}{\epsilon_0}=\frac{\mathrm{Q}}{\epsilon_0} \quad \because \mathrm{Q}=\mathrm{CV} \\<br/>&amp; \therefore \phi=\frac{\mathrm{CV}}{\epsilon_0}<br/>\end{aligned}$</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch0.db
title:
A capillary tube is attached horizontally to a constant heat arrangement. If the radius of the capillary tube is increased by 25% , then the rate of flow of liquid will change nearly by

slug:
a-capillary-tube-is-attached-horizontally-to-a-constant-heat-arrangement-if-the-radius-of-the-capil-55110

question:
<div class="question">A capillary tube is attached horizontally to a constant heat arrangement. If the radius of the capillary tube is increased by $25 \%$, then the rate of flow of liquid will change nearly by</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>$100 \%$
<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>$112 \%$
<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>$124 \%$
<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"> <br/>$144 \%$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>$144 \%$</span> </div>

answer:
<div class="solution">Liquid volume coming out of the tube per second
<br/>$$
<br/>\begin{aligned}
<br/>&amp; \quad V=\frac{p \pi r^4}{8 \eta l} \\
<br/>&amp; \Rightarrow \\
<br/>&amp; \Rightarrow \frac{V_2}{V_1}=\left[\frac{r_2}{r_1}\right]^4 \Rightarrow V_2=V_1\left[\frac{125}{100}\right]^4=V_1\left(\frac{5}{4}\right)^4 \\
<br/>&amp; \Rightarrow \\
<br/>&amp; \text { So, now } \frac{\Delta V}{V}=\frac{V_2-V_1}{V_1}=\frac{(244) V_1-V_1}{V_1}=144 \%
<br/>\end{aligned}
<br/>$$</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch0.db
title:
A capillary tube of radius r is immersed vertically in a liquid such that liquid rises in it to height h (less than the length of the tube). Mass of liquid in the capillary tube is m . If radius of the capillary tube is increased by 50% , then mass of liquid that will rise in the tube, is

slug:
a-capillary-tube-of-radius-r-is-immersed-vertically-in-a-liquid-such-that-liquid-rises-in-it-to-heig-97079

question:
<div class="question">A capillary tube of radius $\mathrm{r}$ is immersed vertically in a liquid such that liquid rises in it to height $\mathrm{h}$ (less than the length of the tube). Mass of liquid in the capillary tube is $\mathrm{m}$. If radius of the capillary tube is increased by $50 \%$, then mass of liquid that will rise in the tube, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{2}{3} \mathrm{~m}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{m}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{3}{2} \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{9}{4} \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{3}{2} \mathrm{~m}$</span> </div>

answer:
<div class="solution">$\mathrm{h}=\frac{2 \mathrm{~T} \cos \theta}{\mathrm{r} \rho \mathrm{g}} \Rightarrow \mathrm{h} \propto \frac{1}{\mathrm{r}} \Rightarrow \frac{\mathrm{h}_{2}}{\mathrm{~h}_{1}}=\frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}=\frac{2}{3}$
<br/> <br/>$$
<br/> <br/>\begin{aligned}
<br/> <br/>\left(\because \mathrm{r}_{1}=\mathrm{r}, \quad \mathrm{r}_{2}\right.&amp;=\mathrm{r}+50 \% \text { of } \left.\mathrm{r}=\frac{3}{2} \mathrm{r}\right) \\
<br/> <br/>\text { New mass } \mathrm{m}_{2}=\pi \mathrm{r}_{2}^{2} \mathrm{~h}_{2} \rho &amp;=\pi\left(\frac{3}{2} \mathrm{r}_{1}\right)^{2}\left(\frac{2}{3} \mathrm{~h}_{1}\right) \rho \\
<br/> <br/>&amp;=\frac{3}{2}\left(\pi \mathrm{r}_{1}^{2} \mathrm{~h}_{1}\right) \rho=\frac{3}{2} \mathrm{~m}
<br/> <br/>\end{aligned}
<br/> <br/>$$</div>


slug: a-carbon-resistor-of-56-5-6-k-is-to-be-marked-with-rings-of-different-colours-for-its-identif-81831
tags: ['Physics', 'Current Electricity', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch0.db
title:
A carbon resistor of 56 Â± 5 . 6 kÎ© is to be marked with rings of different colours for its identification. The colour code sequence will be

question:
<div class="question">A carbon resistor of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>56</mn><mo>±</mo><mn>5</mn><mo>.</mo><mn>6</mn></mrow></mfenced><mo> </mo><mi>kΩ</mi></math> is to be marked with rings of different colours for its identification. The colour code sequence will be</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">green, blue, orange, silver</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">blue, yellow, orange, silver</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">green, red, orange, silver</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">red, green, blue, gold</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">green, blue, orange, silver</span> </div>

answer:
<div class="solution"><p>Given, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mfenced><mrow><mn>56</mn><mo>±</mo><mn>5</mn><mo>.</mo><mn>6</mn></mrow></mfenced><mo> </mo><mi>k</mi><mo> </mo><mi mathvariant="normal">Ω</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>56</mn><mo> </mo><mi mathvariant="normal">k</mi><mo> </mo><mi mathvariant="normal">Ω</mi><mo>±</mo><mn>10</mn><mo> </mo><mo>%</mo></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>56</mn><mo> </mo><mi mathvariant="normal">k</mi><mo> </mo><mi mathvariant="normal">Ω</mi></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>56</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo>±</mo><mn>10</mn><mo> </mo><mo>%</mo><mo> </mo><mi mathvariant="normal">Ω</mi></math></p><p>As per the colour code for carbon resistors, the colour assigned to numbers</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>→</mo></math> Green<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>→</mo></math> Blue<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>→</mo></math> Orange</p><p>For <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mo>%</mo></math> accuracy or tolerance, the colour is silver. Hence, the bands of colours of carbon resistor in sequence are green, blue, orange and silver.</p></div>


slug: a-carnot-s-heat-engine-works-between-the-temperatures-42-7-c-and-2-7-c-what-amount-of-heat-16591
tags: ['Physics', 'Thermodynamics', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch0.db
title:
A Carnot's heat engine works between the temperatures 42 7 â C and 2 7 â C . What amount of heat should it consume per second to deliver mechanical work at the rate of 1.0 kW ?

question:
<div class="question">A Carnot's heat engine works between the temperatures $427^{\circ} \mathrm{C}$ and $27^{\circ} \mathrm{C}$. What amount of heat should it consume per second to deliver mechanical work at the rate of $1.0 \mathrm{~kW} ?$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$0.417 \mathrm{kcal} / \mathrm{s}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$4.17 \mathrm{kcal} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$41.7 \mathrm{kcal} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$0.212 \mathrm{kcal} / \mathrm{s}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.417 \mathrm{kcal} / \mathrm{s}$</span> </div>

answer:
<div class="solution">The efficiency of the heat engine is
<br/> <br/>$$
<br/> <br/>\eta=1-\frac{T_{2}}{T_{1}}=1-\left(\frac{273+27 K}{273+427 K}\right)=\frac{4}{7}
<br/> <br/>$$
<br/> <br/>But $\quad \eta=\frac{\mathrm{W}}{\mathrm{Q}_{1}}$
<br/> <br/>$$
<br/> <br/>\therefore \mathrm{Q}_{1}=\frac{\mathrm{W}}{\eta}=\frac{1.0 \mathrm{~kW}}{4 / 7}=1.75 \mathrm{~kW}=0.417 \mathrm{kcal} / \mathrm{s}
<br/> <br/>$$
<br/> <br/>Thus, the engine would require 417 cal of heat per second, to deliver the requisite amount of work.</div>


slug: a-certain-metal-sulphide-m-s-2-is-used-extensively-as-a-high-temperature-lubricant-if-ms-2-54315
tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch0.db
title:
A certain metal sulphide, M S 2 â , is used extensively as a high temperature lubricant. If MS 2 â is 40.06% by mass sulphur, metal M has atomic mass.

question:
<div class="question">A certain metal sulphide, $M S_2$, is used extensively as a high temperature lubricant. If $\mathrm{MS}_2$ is $40.06 \%$ by mass sulphur, metal $M$ has atomic mass.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>$160 \mathrm{u}$
<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>$64 \mathrm{u}$
<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>$40 \mathrm{u}$
<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"> <br/>$96 \mathrm{u}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>$96 \mathrm{u}$</span> </div>

answer:
<div class="solution">$M S_2=M+32 \times 2=M+64$
<br/>$\%$ of sulphur $=\left(\frac{64}{M+64}\right) \times 100=40.06$
<br/>$M+64=\frac{6400}{40.06}$
<br/>$M+64=160$
<br/>$M=160-64=96$ u</div>


tags: ['Physics', 'Work Power Energy', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch0.db
title:
A chain of mass M is placed on a smooth table with 1/ n of its length L hanging over the edge. The work done in pulling the hanging portion of the chain back to the surface of the table is

slug:
a-chain-of-mass-m-is-placed-on-a-smooth-table-with-1-n-of-its-length-l-hanging-over-the-edge-the-w-16001

question:
<div class="question">A chain of mass $\mathrm{M}$ is placed on a smooth table with $1 / \mathrm{n}$ of its length $\mathrm{L}$ hanging over the edge. The work done in pulling the hanging portion of the chain back to the surface of the table is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{MgL} / \mathrm{n}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{MgL} / 2 \mathrm{n}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{MgL} / \mathrm{n}^{2}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{MgL} / 2 \mathrm{n}^{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{MgL} / 2 \mathrm{n}^{2}$</span> </div>

answer:
<div class="solution">$\quad \mathrm{W}=$ change in $\mathrm{PE}$ of $\mathrm{COM}$ of hanging part<br/>$$<br/>=\frac{\mathrm{M}}{\mathrm{n}} \mathrm{g} \frac{\mathrm{L}}{2 \mathrm{n}}=\frac{\mathrm{MgL}}{2 \mathrm{n}^{2}}<br/>$$</div>


slug: a-charge-particle-is-moving-in-a-uniform-magnetic-field-2-i-3-j-t-if-it-has-an-accel-15654
tags: ['Physics', 'Magnetic Effects of Current', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">6</span> </div>
source_db: MarksBatch0.db
title:
A charge particle is moving in a uniform magnetic field ( 2 i ^ + 3 j ^ â ) T . If it has an acceleration of ( Î± i ^ â 4 j ^ â ) m / s 2 , then the value of Î± will be :

question:
<div class="question">A charge particle is moving in a uniform magnetic field $(2 \hat{i}+3 \hat{j}) \mathrm{T}$. If it has an acceleration of $(\alpha \hat{i}-4 \hat{j}) \mathrm{m} / \mathrm{s}^2$, then the value of $\alpha$ will be :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">3</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">6</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">12</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">2</span> </li> </ul>

answer:
<div class="solution">Given that uniform magnetic field, $\vec{B}=(2 \hat{i}+3 \hat{j}) T$<br/>Acceleration $\vec{a}=(\alpha \hat{i}-4 \hat{j}) \mathrm{m} / \mathrm{s}^2$ We know that<br/>$F=q(\vec{v} \times \vec{B}) \Rightarrow m \vec{a}=q(\vec{v} \times \vec{B})$<br/>Here, $\vec{a} \perp \vec{B}$, so, $\vec{a} \cdot \vec{B}=0$<br/>$(\alpha \hat{i}-4 \hat{j})(2 \hat{i}+3 \hat{j})=0 \Rightarrow 2 \alpha-12=0 \Rightarrow \alpha=6$</div>


slug: a-charge-q-1-exerts-some-force-on-a-second-charge-q-2-if-a-3-rd-charge-q-3-is-brought-56455
tags: ['Physics', 'Electrostatics', 'BITSAT', 'BITSAT 2011']
answer: <div class="solution">No Solution available</div>
source_db: MarksBatch0.db
title:
A charge Q 1 â exerts some force on a second charge Q 2 â . If a 3 rd charge Q 3 â is brought near, then the force of Q 1 â exerted on Q 2 â â

question:
<div class="question">A charge $\mathrm{Q}_{1}$ exerts some force on a second charge $\mathrm{Q}_{2}$. If a 3 rd charge $\mathrm{Q}_{3}$ is brought near, then the force of $\mathrm{Q}_{1}$ exerted on $\mathrm{Q}_{2}-$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">will increase</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">will decrease</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">will remain unchanged</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">will increase if $\mathrm{Q}_{3}$ is of the same sign as $\mathrm{Q}_{1}$ and will decrease if $\mathrm{Q}_{3}$ is of opposite sign.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">will remain unchanged</span> </div>


tags: ['Physics', 'Electrostatics', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch0.db
title:
A charge + q is at a distance L /2 above a square of side L . Then what is the flux linked with the surface?

slug:
a-charge-q-is-at-a-distance-l-2-above-a-square-of-side-l-then-what-is-the-flux-linked-with-the-45275

question:
<div class="question">A charge $+q$ is at a distance $L / 2$ above a square of side $\mathrm{L}$. Then what is the flux linked with the surface?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\mathrm{q}}{4 \varepsilon_{0}}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{2 q}{3 \varepsilon_{0}}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{\mathrm{q}}{6 \varepsilon_{0}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{6 \mathrm{q}}{\varepsilon_{0}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{q}}{6 \varepsilon_{0}}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/yVVO3LpdmZ20CqO6ICa0d7KACe8LFNfQG2cK4diHrEs.original.fullsize.png"/><br/>m{L}
<br/> <br/>The given square of side $L$ may be considered as one of the faces of a cube with edge $L$. Then given charge q will be considered to be placed at the centre of the cube. Then according to Gauss's theorem, the magnitude of the electric flux through the faces (six) of the cube is given by
<br/> <br/>$\phi=\mathrm{q} / \varepsilon_{0}$
<br/> <br/>Hence, electric flux through one face of the cube for the given square will be
<br/> <br/>$\phi^{\prime}=\frac{1}{6} \phi=\frac{\mathrm{q}}{6 \varepsilon_{0}}$</div>


tags: ['Physics', 'Electrostatics', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch0.db
title:
A charge + q is at a distance L /2 above a square of side L . Then what is the flux linked with the surface?

slug:
a-charge-q-is-at-a-distance-l-2-above-a-square-of-side-l-then-what-is-the-flux-linked-with-the-91460

question:
<div class="question">A charge $+q$ is at a distance $L / 2$ above a square of side $\mathrm{L}$. Then what is the flux linked with the surface?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\mathrm{q}}{4 \varepsilon_{0}}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{2 q}{3 \varepsilon_{0}}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{\mathrm{q}}{6 \varepsilon_{0}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{6 \mathrm{q}}{\varepsilon_{0}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{q}}{6 \varepsilon_{0}}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/DsLEBhteUM-6NOBx-ICwRFdm3sbtxNxlWNhELIGFTTQ.original.fullsize.png"/><br/><br/>The given square of side $\mathrm{L}$ may be considered as one of the faces of a cube with edge $\mathrm{L}$. Then given charge $\mathrm{q}$ will be considered to be placed at the centre of the cube. Then according to Gauss's theorem, the magnitude of the electric flux through the faces (six) of the cube is given by<br/>$$<br/>\phi=\mathrm{q} / \varepsilon_{0}<br/>$$<br/>Hence, electric flux through one face of the cube for the given square will be<br/>$\phi^{\prime}=\frac{1}{6} \phi=\frac{\mathrm{q}}{6 \varepsilon_{0}}$</div>


tags: ['Physics', 'Electrostatics', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch0.db
title:
A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other two corners. If the net electrical force on Q is zero, then q Q â equals:

slug:
a-charge-q-is-placed-at-each-of-the-opposite-corners-of-a-square-a-charge-q-is-placed-at-each-of-th-76982

question:
<div class="question">A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the net electrical force on $Q$ is zero, then $\frac{Q}{q}$ equals:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$-1$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$-\frac{1}{\sqrt{2}}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$-2 \sqrt{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-2 \sqrt{2}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/Hts9_DP0I9bJeoH6q8wbY_mrR2-h2VwGI2mzTegRaJc.original.fullsize.png"/><br/> <br/> <br/>It is given that $\vec{F}_{A}+\vec{F}_{B}+\vec{F}_{D}=0$
<br/> <br/>Where $\vec{F}_{A}, \vec{F}_{B}$ and $\vec{F}_{D}$ are the forces applied by charges placed at $A, B$ and $D$ on the charge placed at $C$.
<br/> <br/>$\begin{array}{l}
<br/> <br/>\Rightarrow \overrightarrow{\mathrm{F}}_{\mathrm{B}}+\overrightarrow{\mathrm{F}}_{\mathrm{D}}=-\overrightarrow{\mathrm{F}}_{\mathrm{A}} \\
<br/> <br/>\left|\overrightarrow{\mathrm{F}}_{\mathrm{B}}+\overrightarrow{\mathrm{F}}_{\mathrm{D}}\right|=\sqrt{2} \frac{\mathrm{KqQ}}{\mathrm{a}^{2}} \\
<br/> <br/>\Rightarrow\left|\overrightarrow{\mathrm{F}}_{\mathrm{A}}\right|=\frac{\mathrm{KQ}^{2}}{2 a^{2}} \\
<br/> <br/>\therefore \sqrt{2} \frac{\mathrm{KqQ}}{a^{2}}=-\frac{\mathrm{KQ}^{2}}{2 a^{2}} \\
<br/> <br/>\Rightarrow \frac{\mathrm{Q}}{q}=-2 \sqrt{2}
<br/> <br/>\end{array}$</div>


tags: ['Physics', 'Capacitance', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch0.db
title:
A charged capacitor of capacitance C is discharging through a resistor of resistance R . At what time the charge on the capacitor is equal to one half of its initial value?

slug:
a-charged-capacitor-of-capacitance-c-is-discharging-through-a-resistor-of-resistance-r-at-what-tim-75499

question:
<div class="question">A charged capacitor of capacitance <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math> is discharging through a resistor of resistance <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math>. At what time the charge on the capacitor is equal to one half of its initial value?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>R</mi><mi>C</mi></mrow><mn>2</mn></mfrac></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>R</mi><mi>C</mi></mrow><mrow><msub><mi>log</mi><mi>e</mi></msub><mn>2</mn></mrow></mfrac></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>C</mi><msub><mi>log</mi><mrow><mi>e</mi><mo> </mo></mrow></msub><mn>2</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><mi>R</mi><mi>C</mi></mrow></mfrac><msub><mi>log</mi><mi>e</mi></msub><mn>2</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi>C</mi><msub><mi>log</mi><mrow><mi>e</mi><mo> </mo></mrow></msub><mn>2</mn></math></span> </div>

answer:
<div class="solution"><p>The charge on the capacitor at time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> in a discharging circuit is given by <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><msub><mi>q</mi><mn>0</mn></msub><msup><mi>e</mi><mrow><mo>-</mo><mi>t</mi><mo>/</mo><mi>τ</mi></mrow></msup></math></p><p>where, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>τ</mi><mo>=</mo><mi>R</mi><mi>C</mi><mo>=</mo></math> time constant<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math>               <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><msub><mi>q</mi><mn>0</mn></msub><msup><mi>e</mi><mrow><mo>-</mo><mi>t</mi><mo>/</mo><mi>R</mi><mi>C</mi></mrow></msup></math></p><p>when, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>  </mo><mi>q</mi><mo>=</mo><mfrac><msub><mi>q</mi><mn>0</mn></msub><mn>2</mn></mfrac></math></p><p>then  <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>q</mi><mn>0</mn></msub><mn>2</mn></mfrac><mo>=</mo><msub><mi>q</mi><mn>0</mn></msub><msup><mi>e</mi><mrow><mo>-</mo><mi>t</mi><mo>/</mo><mi>R</mi><mi>C</mi></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><msup><mi>e</mi><mrow><mo>-</mo><mi>t</mi><mo>/</mo><mi>R</mi><mi>C</mi></mrow></msup></math></p><p>Taking natural log on both side <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>log</mi><mi>e</mi></msub><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mo>=</mo><msub><mi>log</mi><mn>0</mn></msub><msup><mi>e</mi><mrow><mo>-</mo><mi>t</mi><mo>/</mo><mi>R</mi><mi>C</mi></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msub><mi>log</mi><mi>e</mi></msub><mn>2</mn><mo>=</mo><mo>-</mo><mfrac><mi>t</mi><mrow><mi>R</mi><mi>C</mi></mrow></mfrac><msub><mi>log</mi><mi>e</mi></msub><mi>e</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>t</mi><mo>=</mo><mi>R</mi><mi>C</mi><msub><mi>log</mi><mi>e</mi></msub><mn>2</mn></math></p></div>


tags: ['Physics', 'Magnetic Effects of Current', 'BITSAT', 'BITSAT 2015']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$2 \%$</span> </div>
source_db: MarksBatch0.db
title:
A charged particle moving in a uniform magnetic field and losses 4% of its kinetic energy. The radius of curvature of its path changes by

slug:
a-charged-particle-moving-in-a-uniform-magnetic-field-and-losses-4-of-its-kinetic-energy-the-radiu-76718

question:
<div class="question">A charged particle moving in a uniform magnetic field and losses $4 \%$ of its kinetic energy. The radius of curvature of its path changes by</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$2 \%$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$4 \%$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$10 \%$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$12 \%$</span> </li> </ul>

answer:
<div class="solution">As we know $\mathrm{F}=\mathrm{qvB}=\frac{\mathrm{mv}^{2}}{\mathrm{r}}$
<br/> <br/>$\therefore \mathrm{r}=\frac{\mathrm{mv}}{\mathrm{Bq}}$
<br/> <br/>And $\mathrm{KE}=\mathrm{k}=\frac{1}{2} \mathrm{mv}^{2}$
<br/> <br/>$\therefore \mathrm{mv}=\sqrt{2 \mathrm{~km}}$
<br/> <br/>$\therefore \mathrm{r}=\frac{\mathrm{mv}}{\mathrm{qB}}=\frac{\sqrt{2 \mathrm{~km}}}{\mathrm{qB}}$
<br/> <br/>$\Rightarrow r \propto \sqrt{k}$ or $r=c^{1 / 2}(c$ is a constant $)$ $\frac{\mathrm{dr}}{\mathrm{dr}}=\mathrm{c} \frac{\mathrm{dk}^{1 / 2}}{\mathrm{dr}}$ or $\frac{\mathrm{c} \Delta \mathrm{k}}{\Delta \mathrm{r}}=2 \sqrt{\mathrm{k}}$
<br/> <br/>$\frac{\Delta r}{r}=\frac{\mathrm{c} \Delta \mathrm{k}}{2 \sqrt{\mathrm{k}} \mathrm{c} \sqrt{\mathrm{k}}}=\frac{\Delta \mathrm{k}}{2 \mathrm{k}}$
<br/> <br/>Therefore percentage changes in radius of path,
<br/> <br/>$\frac{\Delta r}{r} \times 100=\frac{\Delta k}{2 k} \times 100=2 \%$</div>


title: A circle touches both the y -axis and the line x + y = 0 . Then the locus of its center is
slug: a-circle-touches-both-the-y-axis-and-the-line-x-y-0-then-the-locus-of-its-center-is-62605
tags: ['Mathematics', 'Circle', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch0.db
question:
<div class="question">A circle touches both the $y$-axis and the line $x+$ $y=0$. Then the locus of its center is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$y=\sqrt{2} x$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$x=\sqrt{2} y$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$y^2-x^2=2 x y$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$x^2-y^2=2 x y$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$x^2-y^2=2 x y$</span> </div>

answer:
<div class="solution"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/Yy9qTHyHjRgqVFz9Dgt0VVAU50znKoaKw4ER9mQUnug.original.fullsize.png"/><br/><br/>Let $(h, k)$ is centre of circle<br/>$\left|\frac{h-k}{\sqrt{2}}\right|=|h|, k^2-h^2+2 h k=0$</div>


tags: ['Physics', 'Rotational Motion', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch0.db
title:
A circular disc of radius R and thickness 6 R â has moment inertia I about an axis passing through its centre perpendicular to its plane. It is melted and recasted into a solid sphere. The moment of inertia of the sphere about its diameter is

slug:
a-circular-disc-of-radius-r-and-thickness-6-r-has-moment-inertia-i-about-an-axis-passing-through-74024

question:
<div class="question">A circular disc of radius $\mathrm{R}$ and thickness $\frac{R}{6}$ has moment inertia I about an axis passing through its centre perpendicular to its plane. It is melted and recasted into a solid sphere. The moment of inertia of the sphere about its diameter is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$I$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{2 I}{8}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{I}{5}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{I}{10}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{I}{5}$</span> </div>

answer:
<div class="solution">According to problem disc is melted and recasted into a solid sphere so their volume
<br/> <br/>$$
<br/> <br/>\begin{array}{c}
<br/> <br/>\text { will be same. } \\
<br/> <br/>V_{\text {Disc }}=V_{\text {Sphere }} \Rightarrow \pi R_{\text {Disc }}^{2} t=\frac{4}{3} \pi R_{\text {Sphere }}^{3} \\
<br/> <br/>\Rightarrow \pi R_{\text {Disc }}^{2}\left(\frac{R_{\text {Disc }}}{6}\right)=\frac{4}{3} \pi R_{\text {Sphere }}^{3}\left[t=\frac{R_{\text {Disc }}}{6}, \text { given }\right] \\
<br/> <br/>\Rightarrow R_{\text {Disc }}^{3}=8 R_{\text {Sphere }}^{3} \Rightarrow R_{\text {Sphere }}=\frac{R_{\text {Disc }}}{2}
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>Moment of inertia of disc
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>I_{\text {Disc }}=\frac{1}{2} M R_{\text {Disc }}^{2}=I \text { (given) } \\
<br/> <br/>\therefore \text { M }\left(R_{\text {Disc }}\right)^{2}=2 I
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>Moment of inertia of sphere
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>I_{\text {Sphere }}=\frac{1}{2} M R_{\text {Sphere }}^{2} \\
<br/> <br/>=\frac{2}{5} M\left(\frac{R_{\text {Disc }}}{2}\right)^{2}=\frac{M}{10}\left(R_{\text {Disc }}\right)^{2}=\frac{2 I}{10}=\frac{I}{5}
<br/> <br/>\end{array}
<br/> <br/>$$</div>


tags: ['Mathematics', 'Sets and Relations', 'JEE Main']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">60</span> </div>
source_db: MarksBatch0.db
title:
A class has 175 students. The following data shows the number of students obtaining one or more subjects. Mathematics 100 , Physics 70 , Chemistry 40; Mathematics and Physics 30 , Mathematics and Chemistry 28 , Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone?

slug:
a-class-has-175-students-the-following-data-shows-the-number-of-students-obtaining-one-or-more-subj-70881

question:
<div class="question">A class has 175 students. The following data shows the number of students obtaining one or more subjects. Mathematics 100 , Physics 70 , Chemistry 40; Mathematics and Physics 30 , Mathematics and Chemistry 28 , Physics and Chemistry 23; Mathematics, Physics and Chemistry $18 .$ How many students have offered Mathematics alone?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">35</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">48</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">60</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">22</span> </li> </ul>

answer:
<div class="solution">$\begin{aligned} &amp; n(\mathrm{M} \text { alone }) \\ &amp;=n(\mathrm{M})-n(\mathrm{M} \cap \mathrm{C})-n(\mathrm{M} \cap \mathrm{P})+n(\mathrm{M} \cap \mathrm{C} \cap \mathrm{P}) \\ &amp;=100-28-30+18=60 \end{aligned}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/4cmZ9HmBbcB8qSB0F-frwWesAJkLfXEnrdlHo_3SXNQ.original.fullsize.png"/></div>


tags: ['Mathematics', 'Sets and Relations', 'BITSAT', 'BITSAT 2013']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">60</span> </div>
source_db: MarksBatch0.db
title:
A class has 175 students. The following data shows the number of students obtaining one or more subjects. Mathematics 100 , Physics 70 , Chemistry 40; Mathematics and Physics 30 , Mathematics and Chemistry 28 , Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone?

slug:
a-class-has-175-students-the-following-data-shows-the-number-of-students-obtaining-one-or-more-subj-72920

question:
<div class="question">A class has 175 students. The following data shows the number of students obtaining one or more subjects. Mathematics 100 , Physics 70 , Chemistry 40; Mathematics and Physics 30 , Mathematics and Chemistry 28 , Physics and Chemistry 23; Mathematics, Physics and Chemistry $18 .$ How many students have offered Mathematics alone?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">35</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">48</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">60</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">22</span> </li> </ul>

answer:
<div class="solution">$\begin{aligned} &amp; n(\mathrm{M} \text { alone }) \\ &amp;=n(\mathrm{M})-n(\mathrm{M} \cap \mathrm{C})-n(\mathrm{M} \cap \mathrm{P})+n(\mathrm{M} \cap \mathrm{C} \cap \mathrm{P}) \\ &amp;=100-28-30+18=60 \end{aligned}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/4cmZ9HmBbcB8qSB0F-frwWesAJkLfXEnrdlHo_3SXNQ.original.fullsize.png"/></div>


tags: ['Physics', 'Electromagnetic Induction', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch0.db
title:
A coil 10 turns and a resistance of 20Î© is connected in series with B.G of resistance 30Î© . The coil is placed with its plane perpendicular to the direction of a uniform magnetic field of induction 1 0 â 2 T . If it is now turned through an angle of 6 0 â about an axis in its plane. Find the charge induced in the coil. (Area of a coil = 1 0 â 2 m 2 )

slug:
a-coil-10-turns-and-a-resistance-of-20-is-connected-in-series-with-b-g-of-resistance-30-the-co-59472

question:
<div class="question">A coil 10 turns and a resistance of $20 \Omega$ is connected in series with B.G of resistance $30 \Omega$. The coil is placed with its plane perpendicular to the direction of a uniform magnetic field of induction $10^{-2} \mathrm{~T}$. If it is now turned through an angle of $60^{\circ}$ about an axis in its plane. Find the charge induced in the coil. (Area of a coil $=10^{-2} \mathrm{~m}^{2}$ )</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 \times 10^{-5} \mathrm{C}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$3.2 \times 10^{-5} \mathrm{C}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$1 \times 10^{-5} \mathrm{C}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$5.5 \times 10^{-5} \mathrm{C}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1 \times 10^{-5} \mathrm{C}$</span> </div>

answer:
<div class="solution">Given: $\mathrm{n}=10$ turns, $\mathrm{R}_{\text {coil }}=20 \Omega, \mathrm{R}_{\mathrm{G}}=30 \Omega$, Total resistance in the circuit $=20+30$
<br/> <br/>$=50 \Omega$
<br/> <br/>$\mathrm{A}=10^{-2} \mathrm{~m}^{2}, \mathrm{~B}=10^{-2} \mathrm{~T}, \phi_{1}=0^{\circ}, \phi_{2}=60^{\circ}$
<br/> <br/>$\mathrm{q}=\frac{\phi_{1}-\phi_{2}}{\mathrm{R}}=\frac{\mathrm{Bn} \mathrm{A} \cos \theta_{1}-\mathrm{Bn} \mathrm{A} \cos \theta_{2}}{\mathrm{R}}$
<br/> <br/>$=\frac{\operatorname{Bn} \mathrm{A}(\cos 0-\cos 60)}{\mathrm{R}}=\frac{\mathrm{BnA}(1-0.5)}{\mathrm{R}}$
<br/> <br/>$=\frac{0.5 \times 10^{-2} \times 10 \times 10^{-2}}{50}=\frac{50 \times 10^{-5}}{50}$
<br/> <br/>$=1 \times 10^{-5} \mathrm{C} \quad$ (Charge induced in a coil)</div>


tags: ['Physics', 'Alternating Current', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch0.db
title:
A coil has resistance 30 ohm and inductive reactance 20 ohm at 50 Hz frequency. If an ac source, of 200 volt, 100 Hz , is connected across the coil, the current in the coil will be

slug:
a-coil-has-resistance-30-ohm-and-inductive-reactance-20-ohm-at-50-hz-frequency-if-an-ac-source-of-18957

question:
<div class="question">A coil has resistance 30 ohm and inductive reactance 20 ohm at $50 \mathrm{~Hz}$ frequency. If an ac source, of 200 volt, $100 \mathrm{~Hz},$ is connected across the coil, the current in the coil will be</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$4.0 \mathrm{~A}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$8.0 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$7.2 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2.0 \mathrm{~A}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$4.0 \mathrm{~A}$</span> </div>

answer:
<div class="solution">If $\omega=50 \times 2 \pi$ then $\omega \mathrm{L}=20 \Omega$ If $\omega^{\prime}=100 \times 2 \pi$ then $\omega^{\prime} \mathrm{L}=40 \Omega$<br/>Current flowing in the coil is<br/>$$<br/>\mathrm{I}=\frac{200}{\mathrm{Z}}=\frac{200}{\sqrt{\mathrm{R}^{2}+\left(\omega^{\prime} \mathrm{L}\right)^{2}}}=4 \mathrm{~A}<br/>$$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch0.db
title:
A coil in the shape of an equilateral triangle of side l is suspended between the pole pieces of a permanent magnet such that B is in plane of the coil. If due to a current i in the triangle, a torque Ï rests on it, the side l of the triangle is

slug:
a-coil-in-the-shape-of-an-equilateral-triangle-of-side-l-is-suspended-between-the-pole-pieces-of-a-p-23197

question:
<div class="question">A coil in the shape of an equilateral triangle of side <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math> is suspended between the pole pieces of a permanent magnet such that <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> is in plane of the coil. If due to a current <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math> in the triangle, a torque <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>τ</mi></math> rests on it, the side <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math> of the triangle is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mfenced><mfrac><mi>τ</mi><mrow><msqrt><mn>3</mn></msqrt><mi>B</mi><mi>i</mi></mrow></mfrac></mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></msup></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>2</mn><msqrt><mn>3</mn></msqrt></mfrac><mfenced><mfrac><mi>τ</mi><mrow><mi>B</mi><mi>i</mi></mrow></mfrac></mfenced></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><span style="color:null;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mfenced><mfrac><mi>τ</mi><mrow><mi>B</mi><mi>i</mi></mrow></mfrac></mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></msup></math></span></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><msqrt><mn>3</mn></msqrt></mfrac><mfenced><mfrac><mi>τ</mi><mrow><mi>B</mi><mi>i</mi></mrow></mfrac></mfenced></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mfenced><mfrac><mi>τ</mi><mrow><msqrt><mn>3</mn></msqrt><mi>B</mi><mi>i</mi></mrow></mfrac></mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></msup></math></span> </div>

answer:
<div class="solution"><p>Torque acting on equilateral triangle in a magnetic field <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> is</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>τ</mi><mo>=</mo><mi>i</mi><mo> </mo><mi>A</mi><mi>B</mi><mo> </mo><mi>sin</mi><mo> </mo><mi>θ</mi></math></p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/37d03392-518a-49a8-9339-d8c73454232d-image.png" style="width: 260px; height: 248px;"/></p><p>Area of triangle <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LMN</mi></math>,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac><msup><mi>l</mi><mn>2</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mn>90</mn><mo>°</mo></math></p><p>Substituting the given values in expression for torque, we get</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>τ</mi><mo>=</mo><mi>i</mi><mo>×</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>4</mn></mfrac><mo> </mo><msup><mi>l</mi><mn>2</mn></msup><mo> </mo><mi>B</mi><mo> </mo><mi>sin</mi><mo> </mo><mn>90</mn><mo>°</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>τ</mi><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>4</mn></mfrac><mi>i</mi><msup><mi>l</mi><mn>2</mn></msup><mi>B</mi></math>    <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>∵</mo><mo> </mo><mo> </mo><mi>sin</mi><mo> </mo><mn>90</mn><mo>°</mo><mo>=</mo><mn>1</mn></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>l</mi><mn>2</mn></msup><mo>=</mo><mfrac><mrow><mn>4</mn><mi>τ</mi></mrow><mrow><msqrt><mn>3</mn></msqrt><mo> </mo><mi>B</mi><mi>i</mi></mrow></mfrac></math></p><p>Here, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>2</mn><mo> </mo><msup><mfenced><mfrac><mi>τ</mi><mrow><msqrt><mn>3</mn></msqrt><mo> </mo><mi>B</mi><mi>i</mi></mrow></mfrac></mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></msup></math></p></div>


tags: ['Mathematics', 'Probability', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch0.db
title:
A coin is tossed 7 times. Each time a man calls head. Find the probability that he wins the toss on more occasions.

slug:
a-coin-is-tossed-7-times-each-time-a-man-calls-head-find-the-probability-that-he-wins-the-toss-on-75523

question:
<div class="question">A coin is tossed 7 times. Each time a man calls head. Find the probability that he wins the toss on more occasions.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{2}{3}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{1}{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{3}{4}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{2}$</span> </div>

answer:
<div class="solution">The man has to win at least 4 times.
<br/> <br/>$$
<br/> <br/>\begin{array}{r}
<br/> <br/>\therefore \text { Reqd. probability }= \\
<br/> <br/>\qquad \begin{array}{r}
<br/> <br/>7 \mathrm{C}_{4}\left(\frac{1}{2}\right)^{4} \cdot\left(\frac{1}{2}\right)^{3}+{ }^{7} \mathrm{C}_{5}\left(\frac{1}{2}\right)^{5} \cdot\left(\frac{1}{2}\right)^{2} \\
<br/> <br/>+{ }^{7} \mathrm{C}_{6}\left(\frac{1}{2}\right)^{6} \cdot \frac{1}{2}+{ }^{7} \mathrm{C}_{7}\left(\frac{1}{2}\right)^{7} \\
<br/> <br/>=\left({ }^{7} \mathrm{C}_{4}+{ }^{7} \mathrm{C}_{5}+{ }^{7} \mathrm{C}_{6}+{ }^{7} \mathrm{C}_{7}\right) \cdot \frac{1}{2^{7}}=\frac{64}{2^{7}}=\frac{1}{2}
<br/> <br/>\end{array}
<br/> <br/>\end{array}
<br/> <br/>$$</div>


tags: ['Mathematics', 'Probability', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch0.db
title:
A coin is tossed 7 times. Each time a man calls head. The probability that he wins the toss at least four times is

slug:
a-coin-is-tossed-7-times-each-time-a-man-calls-head-the-probability-that-he-wins-the-toss-at-least-75624

question:
<div class="question">A coin is tossed <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math> times. Each time a man calls head. The probability that he wins the toss at least four times is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>4</mn></mfrac></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>8</mn></mfrac></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>6</mn></mfrac></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></span> </div>

answer:
<div class="solution"><p>The man has to win atleast <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> times.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Required probability</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mmultiscripts><mi>C</mi><mn>4</mn><none></none><mprescripts></mprescripts><none></none><mn>7</mn></mmultiscripts><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>4</mn></msup><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>3</mn></msup><mo>+</mo><mmultiscripts><mi>C</mi><mn>5</mn><none></none><mprescripts></mprescripts><none></none><mn>7</mn></mmultiscripts><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>5</mn></msup><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>2</mn></msup><mo>+</mo><mmultiscripts><mi>C</mi><mn>6</mn><none></none><mprescripts></mprescripts><none></none><mn>7</mn></mmultiscripts><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>6</mn></msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mo>+</mo><mmultiscripts><mi>C</mi><mn>7</mn><none></none><mprescripts></mprescripts><none></none><mn>7</mn></mmultiscripts><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>7</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfenced><mrow><mmultiscripts><mi>C</mi><mn>4</mn><none></none><mprescripts></mprescripts><none></none><mn>7</mn></mmultiscripts><mo>+</mo><mmultiscripts><mi>C</mi><mn>5</mn><none></none><mprescripts></mprescripts><none></none><mn>7</mn></mmultiscripts><mo>+</mo><mmultiscripts><mi>C</mi><mn>6</mn><none></none><mprescripts></mprescripts><none></none><mn>7</mn></mmultiscripts><mo>+</mo><mmultiscripts><mi>C</mi><mn>7</mn><none></none><mprescripts></mprescripts><none></none><mn>7</mn></mmultiscripts></mrow></mfenced><mo>×</mo><mfrac><mn>1</mn><msup><mn>2</mn><mn>7</mn></msup></mfrac><mo>=</mo><mfrac><mn>64</mn><msup><mn>2</mn><mn>7</mn></msup></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></p></div>


title: A coin is tossed twice. Then, the probability that atleast one tail occurs is
slug: a-coin-is-tossed-twice-then-the-probability-that-atleast-one-tail-occurs-is-45990
tags: ['Mathematics', 'Probability', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch0.db
question:
<div class="question">A coin is tossed twice. Then, the probability that atleast one tail occurs is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{4}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{3}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{3}{4}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{3}{4}$</span> </div>

answer:
<div class="solution">The sample space is $\mathrm{S}=\{\mathrm{HH}, \mathrm{HT}, \mathrm{TH}, \mathrm{TT}\}$<br/>Let $\mathrm{E}$ be the event of getting atleast one tail<br/>$\begin{aligned}<br/>&amp; \therefore \mathrm{E}=\{\mathrm{HT}, \mathrm{TH}, \mathrm{TT}\} \\<br/>&amp; \therefore \text { Required probability } \mathrm{p} \\<br/>&amp; =\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }}=\frac{\mathrm{n}(\mathrm{E})}{\mathrm{n}(\mathrm{S})}=\frac{3}{4}<br/>\end{aligned}$</div>


tags: ['Physics', 'Semiconductors', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch0.db
title:
A common emitter amplifier has a voltage gain of 50 , an input impedance of 100 Î© and an output impedance of 200 Î© . The power gain of the amplifier is

slug:
a-common-emitter-amplifier-has-a-voltage-gain-of-50-an-input-impedance-of-100-and-an-output-imp-64688

question:
<div class="question">A common emitter amplifier has a voltage gain of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math>, an input impedance of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math> and an output impedance of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math>. The power gain of the amplifier is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1250</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1250</mn></math></span> </div>

answer:
<div class="solution"><p>Voltage gain <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi mathvariant="normal">β</mi><mo>×</mo></math> impedance gain</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mn>50</mn><mo>=</mo><mi mathvariant="normal">β</mi><mo>×</mo><mfrac><mn>200</mn><mn>100</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mi mathvariant="normal">β</mi><mo>=</mo><mn>25</mn></math></p><p>Also power gain <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msup><mi mathvariant="normal">β</mi><mn>2</mn></msup><mo>×</mo></math> impedance gain </p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msup><mfenced><mn>25</mn></mfenced><mn>2</mn></msup><mo>×</mo><mfrac><mn>200</mn><mn>100</mn></mfrac><mo>=</mo><mn>1250</mn></math></p></div>


tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'BITSAT', 'BITSAT 2016']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">6</span> </div>
source_db: MarksBatch0.db
title:
A compound of Xe and F is found to have 53.5% of Xe. What is oxidation number of Xe in this compound?

slug:
a-compound-of-xe-and-f-is-found-to-have-53-5-of-xe-what-is-oxidation-number-of-xe-in-this-compound-20801

question:
<div class="question">A compound of Xe and $\mathrm{F}$ is found to have $53.5 \%$ of Xe. What is oxidation number of Xe in this compound?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">-4</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">0</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">4</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">6</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">$\mathrm{Xe}=53.5 \% \therefore \mathrm{F}=46.5 \%$
<br/> <br/>Relative number of atoms Xe
<br/> <br/>$$
<br/> <br/>=\frac{53.5}{131.2}=0.4 \text { and } \mathrm{F}=\frac{46.5}{19}=2.4
<br/> <br/>$$
<br/> <br/>Simple ratio $\mathrm{Xe}=1$ and $\mathrm{F}=6 ;$ Molecular formula is $\mathrm{XeF}_{6}$
<br/> <br/>O. $\mathrm{N}$.of $\mathrm{Xe}$ is +6</div>


tags: ['Physics', 'Electromagnetic Induction', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch0.db
title:
A conducting circular loop is placed in a uniform magnetic field, B = 0 . 025 T with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of 1 mm s - 1 . The induced emf when the radius is 2 cm , is

slug:
a-conducting-circular-loop-is-placed-in-a-uniform-magnetic-field-b-0-025-t-with-its-plane-perpe-76907

question:
<div class="question">A conducting circular loop is placed in a uniform magnetic field, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>025</mn><mo> </mo><mi mathvariant="normal">T</mi></math> with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi>mm</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>. The induced emf when the radius is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi>cm</mi></math>, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>π</mi><mo> </mo><mi>μV</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>π</mi><mo> </mo><mi>μV</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi mathvariant="normal">π</mi><mn>2</mn></mfrac><mi>μV</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi>μV</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>π</mi><mo> </mo><mi>μV</mi></math></span> </div>

answer:
<div class="solution"><p>Here, magnetic field,<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>025</mn><mo> </mo><mi mathvariant="normal">T</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Magnetic flux <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi><mo>=</mo><mi>B</mi><mo>·</mo><mi>A</mi><mo>=</mo><mi>B</mi><mo>·</mo><mi>π</mi><msup><mi>r</mi><mn>2</mn></msup></math></p><p>Induced <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>emf</mi><mo> </mo><mfenced close="|" open="|"><mi mathvariant="normal">e</mi></mfenced><mo>=</mo><mfrac><mrow><mi>d</mi><mi>ϕ</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>B</mi><mi>π</mi><mn>2</mn><mi>r</mi><mo>·</mo><mfrac><mrow><mi>d</mi><mi>r</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>025</mn><mo>×</mo><mi>π</mi><mo>×</mo><mn>2</mn><mo>×</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>×</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>π</mi><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn><mo> </mo></mrow></msup><mo> </mo><mi mathvariant="normal">V</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>π</mi><mo> </mo><mi>μV</mi></math></p></div>


tags: ['Physics', 'Electromagnetic Induction', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch0.db
title:
A conducting circular loop is placed in a uniform magnetic field of 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm / s . The induced emf in the loop when the radius is 2 cm is

slug:
a-conducting-circular-loop-is-placed-in-a-uniform-magnetic-field-of-0-04-t-with-its-plane-perpendicu-20498

question:
<div class="question">A conducting circular loop is placed in a uniform magnetic field of $0.04 \mathrm{~T}$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at $2 \mathrm{~mm} / \mathrm{s}$. The induced emf in the loop when the radius is $2 \mathrm{~cm}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$4.8 \pi \mu \mathrm{V}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.8 \pi \mu \mathrm{V}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1.6 \pi \mu \mathrm{V}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$3.2 \pi \mu \mathrm{V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$3.2 \pi \mu \mathrm{V}$</span> </div>

answer:
<div class="solution">Induced emf in the loop is given by
<br/> <br/>$\mathrm{e}=-\mathrm{B} \cdot \frac{\mathrm{d} \mathrm{A}}{\mathrm{dt}}$ where $\mathrm{A}$ is the area of the loop.
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\mathrm{e}=-\mathrm{B} \cdot \frac{\mathrm{d}}{\mathrm{dt}}\left(\pi \mathrm{r}^{2}\right)=-\mathrm{B} \pi 2 \mathrm{r} \frac{\mathrm{dr}}{\mathrm{dt}} \\
<br/> <br/>\mathrm{r}=2 \mathrm{~cm}=2 \times 10^{-2} \mathrm{~m} \\
<br/> <br/>\mathrm{dr}=2 \mathrm{~mm}=2 \times 10^{-3} \mathrm{~m} \\
<br/> <br/>\mathrm{dt}=1 \mathrm{~s} \\
<br/> <br/>\mathrm{e}=-0.04 \times 3.14 \times 2 \times 2 \times 10^{-2} \times \frac{2 \times 10^{-3}}{1} \mathrm{~V} \\
<br/> <br/>=0.32 \pi \times 10^{-5} \mathrm{~V} \\
<br/> <br/>=3.2 \pi \times 10^{-6} \mathrm{~V} \\
<br/> <br/>=3.2 \pi \mu \mathrm{V}
<br/> <br/>\end{array}
<br/> <br/>$$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'BITSAT', 'BITSAT 2009']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">zero</span> </div>
source_db: MarksBatch0.db
title:
A conducting circular loop of radius r carries a constant current i . It is placed in a uniform magnetic field B 0 â such that B 0 â is perpendicular to the plane of the loop. The magnetic force acting on the loop is

slug:
a-conducting-circular-loop-of-radius-r-carries-a-constant-current-i-it-is-placed-in-a-uniform-magn-38291

question:
<div class="question">A conducting circular loop of radius $r$ carries a constant current $i .$ It is placed in a uniform magnetic field $\overrightarrow{\mathrm{B}}_{0}$ such that $\overrightarrow{\mathrm{B}}_{0}$ is perpendicular to the plane of the loop. The magnetic force acting on the loop is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$i r \mathrm{~B}_{0}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 \pi i r \mathrm{~B}_{0}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">zero</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\pi$ ir $\mathrm{B}_{0}$</span> </li> </ul>

answer:
<div class="solution">The magnetic field is perpendicular to the plane of the paper. Let us consider two diametrically opposite elements. By Fleming's Left hand rule on element $\mathrm{AB}$ the direction of force will be Leftwards and the magnitude will be<br/>$$<br/>\mathrm{dF}=\operatorname{Idl} \mathrm{B} \sin 90^{\circ}=\mathrm{IdIB}<br/>$$<img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/XBTY49ILQHjW94fWn2TJCWNCt3sba5dlj7-xHNKczf4.original.fullsize.png"/></div>


slug: a-conducting-loop-of-radius-10-cm-is-placed-perpendicular-to-a-uniform-magnetic-field-of-14126
tags: ['Physics', 'Electromagnetic Induction', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch0.db
title:
A conducting loop of radius Ï â 10 â cm is placed perpendicular to a uniform magnetic field of 0.5 T . The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25 s is:

question:
<div class="question">A conducting loop of radius $\frac{10}{\sqrt{\pi}} \mathrm{cm}$ is placed perpendicular to a uniform magnetic field of $0.5 T$. The magnetic field is decreased to zero in $0.5 s$ at a steady rate. The induced emf in the circular loop at $0.25 s$ is:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{emf}=1 \mathrm{mV}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{emf}=10 \mathrm{mV}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{emf}=100 \mathrm{mV}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{emf}=5 \mathrm{mV}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{emf}=10 \mathrm{mV}$</span> </div>

answer:
<div class="solution">As $\left.\varepsilon\right|_{t=0.5 \mathrm{sec}}=-\frac{\mathrm{d} \phi}{\mathrm{dt}}$<br/>$=-\mathrm{A} \frac{\mathrm{dB}}{\mathrm{dt}} \quad\left[\because \theta=0^{\circ} \Rightarrow \cos \theta=1\right]$<br/>$=-\pi \times\left(\frac{10}{\sqrt{\pi}}\right)^2 \times 10^{-4} \times \frac{0-0.5}{0.5}=10^{-2} \mathrm{~V}=10 \mathrm{mV}$<br/>As $\frac{d B}{d t}=$ constant $\Rightarrow$ Induced emf will not change with time. So, $\left.\mathrm{e}\right|_{0,5 \mathrm{sec}}=\left.\mathrm{e}\right|_{0.25 \mathrm{sec}}=10 \mathrm{mV}$</div>


tags: ['Physics', 'Electromagnetic Induction', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch0.db
title:
A conducting square loop is placed in a magnetic field B with its plane perpendicular to the field. The sides of the loop start shrinking at a constant rate Î± . The induced emf in the loop at an instant when its side is ' a ' is

slug:
a-conducting-square-loop-is-placed-in-a-magnetic-field-b-with-its-plane-perpendicular-to-the-field-37002

question:
<div class="question">A conducting square loop is placed in a magnetic field $B$ with its plane perpendicular to the field. The sides of the loop start shrinking at a constant rate $\alpha$. The induced emf in the loop at an instant when its side is ' $a$ ' is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$2 a \alpha B$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$a^{2} \alpha B$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2 a^{2} \alpha B$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$a \alpha B$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2 a \alpha B$</span> </div>

answer:
<div class="solution">At any time $t$, the side of the square $a=\left(a_{0}\right.$ $-\alpha t),$ where $a_{0}=$ side at $t=0$
<br/> <br/>At this instant, flux through the square :
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\phi=B A \cos 0^{\circ}=B\left(a_{0}-\alpha t\right)^{2} \\
<br/> <br/>\therefore \text { emf induced } E=-\frac{d \phi}{d t} \\
<br/> <br/>\Rightarrow E=-B .2\left(a_{0}-\alpha t\right)(0-\alpha)=+2 \alpha a B
<br/> <br/>\end{array}
<br/> <br/>$$</div>


tags: ['Physics', 'Electromagnetic Induction', 'BITSAT', 'BITSAT 2020']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">zero</span> </div>
source_db: MarksBatch0.db
title:
A conducting square loop of side L and resistance R moves in its plane with a uniform velocity v perpendicular to one of its side. A magnetic induction B constant in time and space, pointing perpendicular and into the plane of the loop exists everywhere. The current induced in the loop is

slug:
a-conducting-square-loop-of-side-l-and-resistance-r-moves-in-its-plane-with-a-uniform-velocity-v-per-61086

question:
<div class="question">A conducting square loop of side $\mathrm{L}$ and resistance $\mathrm{R}$ moves in its plane with a uniform velocity v perpendicular to one of its side. A magnetic induction $\mathrm{B}$ constant in time and space, pointing perpendicular and into the plane of the loop exists everywhere.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/v3-1Mt3mK4D2OS5PERmiMAk_YvGxnqyAuKIeBkon8vw.original.fullsize.png"/><br/> <br/> <br/>The current induced in the loop is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\mathrm{B} \ell \mathrm{v}}{\mathrm{R}}$ clockwise</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\mathrm{B} \ell \mathrm{v}}{\mathrm{R}}$ anticlockwise</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{2 \mathrm{~B} \ell v}{\mathrm{R}}$ anticlockwise</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">zero</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">Since the magnetic field is uniform the flux $f$ through the square loop at any time $t$ is constant, because
<br/> <br/>$\begin{array}{l}
<br/> <br/>\mathrm{f}=\mathrm{B} \times \mathrm{A}=\mathrm{B} \times \mathrm{L}^{2}=\text { constant } \\
<br/> <br/>\therefore \varepsilon=-\frac{\mathrm{d} \phi}{\mathrm{dt}}=\text { zero }
<br/> <br/>\end{array}$</div>


tags: ['Physics', 'Rotational Motion', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch0.db
title:
A constant torque of 31.4 N â m is exerted on a pivoted wheel. If angular acceleration of wheel is 4 Ï rad / s 2 , then the moment of inertia of the wheel is

slug:
a-constant-torque-of-31-4-n-m-is-exerted-on-a-pivoted-wheel-if-angular-acceleration-of-wheel-is-49154

question:
<div class="question">A constant torque of $31.4 \mathrm{~N}-\mathrm{m}$ is exerted on a pivoted wheel. If angular acceleration of wheel is $4 \pi \mathrm{rad} / \mathrm{s}^{2},$ then the moment of inertia of the wheel is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$2.5 \mathrm{~kg} \mathrm{~m}^{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$3.5 \mathrm{~kg} \mathrm{~m}^{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$4.5 \mathrm{~kg} \mathrm{~m}^{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$5.5 \mathrm{~kg} \mathrm{~m}^{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2.5 \mathrm{~kg} \mathrm{~m}^{2}$</span> </div>

answer:
<div class="solution">$I=\frac{\tau}{\alpha}=\frac{31.4}{4 \pi}=\frac{31.4}{4 \times 3.14}=2.5 \mathrm{~kg} \mathrm{~m}^{2}$.</div>


tags: ['Physics', 'Current Electricity', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch0.db
title:
A constant voltage is applied between the two ends of a uniform metallic wire. Some heat is developed in it. The heat developed is doubled if

slug:
a-constant-voltage-is-applied-between-the-two-ends-of-a-uniform-metallic-wire-some-heat-is-develope-82353

question:
<div class="question">A constant voltage is applied between the two ends of a uniform metallic wire. Some heat is developed in it. The heat developed is doubled if</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">both the length and the radius of the wire are halved.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">both the length and the radius of the wire are doubled.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">the radius of the wire is doubled.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">the length of the wire is doubled.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">both the length and the radius of the wire are doubled.</span> </div>

answer:
<div class="solution">The heat produced is given by
<br/> <br/>$$
<br/> <br/>H=\frac{V^{2}}{R} \text { and } R=\frac{\rho \ell}{\pi r^{2}}
<br/> <br/>$$
<br/> <br/>$\therefore H=V^{2}\left(\frac{\pi r^{2}}{\rho \ell}\right)$
<br/> <br/>or $\quad H=\left(\frac{\pi V^{2}}{\rho}\right) \frac{r^{2}}{\ell}$
<br/> <br/>Thus heat $(H)$ is doubled if both length $(\ell)$ and radius $(r)$ are doubled.</div>


tags: ['Physics', 'Ray Optics', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch0.db
title:
A convex lens of focal length 25 cm produces images of the same magnification 2 , when an object is kept at two positions x 1 and x 2 x 1 > x 2 from the lens. The ratio of x 2 and x 1 is

slug:
a-convex-lens-of-focal-length-25-cm-produces-images-of-the-same-magnification-2-when-an-object-is-33382

question:
<div class="question">A convex lens of focal length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo> </mo><mi>cm</mi></math> produces images of the same magnification <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math>, when an object is kept at two positions <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>1</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>2</mn></msub></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>x</mi><mn>1</mn></msub><mo>&gt;</mo><msub><mi>x</mi><mn>2</mn></msub></mrow></mfenced></math> from the lens. The ratio of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>1</mn></msub></math> is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>:</mo><mn>1</mn></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>:</mo><mn>3</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>:</mo><mn>2</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>:</mo><mn>1</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>:</mo><mn>3</mn></math></span> </div>

answer:
<div class="solution"><p>For the given convex lens, focal length, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>25</mn><mo> </mo><mi>cm</mi></math></p><p>Magnification of lens in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math> is given by,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfrac><mi>f</mi><mrow><mi>f</mi><mo>+</mo><mi>u</mi></mrow></mfrac><mo>=</mo><mfrac><mn>25</mn><mrow><mn>25</mn><mo>+</mo><mi>u</mi></mrow></mfrac><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mi mathvariant="normal">i</mi></mfenced></math></p><p>When the image is real, then <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mo>-</mo><mn>2</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mo>-</mo><msub><mi>x</mi><mn>1</mn></msub></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> From Eq. <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">i</mi><mo>)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>=</mo><mfrac><mn>25</mn><mrow><mn>25</mn><mo>-</mo><msub><mi>x</mi><mn>1</mn></msub></mrow></mfrac><mo>⇒</mo><msub><mi>x</mi><mn>1</mn></msub><mo>=</mo><mfrac><mn>75</mn><mn>2</mn></mfrac></math></p><p>Again, when the image is virtual, then <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mn>2</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mo>-</mo><msub><mi>x</mi><mn>2</mn></msub></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> From Eq. <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi mathvariant="normal">i</mi><mo>)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>=</mo><mfrac><mn>25</mn><mrow><mn>25</mn><mo>-</mo><msub><mi>x</mi><mn>2</mn></msub></mrow></mfrac><mo>⇒</mo><msub><mi>x</mi><mn>2</mn></msub><mo>=</mo><mfrac><mn>25</mn><mn>2</mn></mfrac></math></p><p>Hence, the ratio of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>2</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>1</mn></msub></math> is</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mfrac><msub><mi>x</mi><mn>2</mn></msub><msub><mi>x</mi><mn>1</mn></msub></mfrac><mo>=</mo><mfrac><mrow><mn>25</mn><mo>/</mo><mn>2</mn></mrow><mrow><mn>75</mn><mo>/</mo><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></math></p></div>


tags: ['Physics', 'Ray Optics', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch0.db
title:
A convex lens shown in the figure is made up of two types of transparent materials. A point sources of light is placed on its principal axis. If reflections from the boundaries between layers are ignored, the lens will form

slug:
a-convex-lens-shown-in-the-figure-is-made-up-of-two-types-of-transparent-materials-a-point-sources-66864

question:
<div class="question">A convex lens shown in the figure is made up of two types of transparent materials. A point sources of light is placed on its principal axis. If reflections from the boundaries between layers are ignored, the lens will form<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/9d490464-232a-4a92-a368-eb213a0feddd-image.png" style="width: 90px; height: 261px;"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">only one image</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">two images</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">infinite images</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">no image at all</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">two images</span> </div>

answer:
<div class="solution">Since, the lens is made up of two kinds of transparent material, it has two refractive indices for the incident beam of light. Hence, there will be two focal lengths of the lens and therefore two images will be observed.</div>


tags: ['Physics', 'Magnetic Effects of Current', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch0.db
title:
A copper rod of mass m slides under gravity on two smooth parallel rails l distance apart and set an angle Î¸ to the horizontal. At the bottom, the rails are joined by a resistance R in figure. There is a uniform magnetic field B perpendicular to the plane of the rails. The terminal velocity of rod is

slug:
a-copper-rod-of-mass-m-slides-under-gravity-on-two-smooth-parallel-rails-l-distance-apart-and-set-an-60010

question:
<div class="question"><p>A copper rod of mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> slides under gravity on two smooth parallel rails <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math> distance apart and set an angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> to the horizontal. At the bottom, the rails are joined by a resistance <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> in figure. There is a uniform magnetic field <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> perpendicular to the plane of the rails. The terminal velocity of rod is</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/f9f90ec0-b008-4e91-bc69-94f4537499cc-image.png" style="width: 200px; height: 181px;"/></p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>m</mi><mi>g</mi><mi>R</mi><mi>tan</mi><mi>θ</mi></mrow><mrow><msup><mi>B</mi><mn>2</mn></msup><msup><mi>l</mi><mn>2</mn></msup></mrow></mfrac></math></p></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>m</mi><mi>g</mi><mi>R</mi><mi>cot</mi><mi>θ</mi></mrow><mrow><msup><mi>B</mi><mn>2</mn></msup><msup><mi>l</mi><mn>2</mn></msup></mrow></mfrac></math></p></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>m</mi><mi>g</mi><mi>R</mi><mi>sin</mi><mi>θ</mi></mrow><mrow><msup><mi>B</mi><mn>2</mn></msup><msup><mi>l</mi><mn>2</mn></msup></mrow></mfrac></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>m</mi><mi>g</mi><mi>R</mi><mi>cos</mi><mi>θ</mi></mrow><mrow><msup><mi>B</mi><mn>2</mn></msup><msup><mi>l</mi><mn>2</mn></msup></mrow></mfrac></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>m</mi><mi>g</mi><mi>R</mi><mi>sin</mi><mi>θ</mi></mrow><mrow><msup><mi>B</mi><mn>2</mn></msup><msup><mi>l</mi><mn>2</mn></msup></mrow></mfrac></math></span> </div>

answer:
<div class="solution"><p>Terminal velocity of the rod is attained when magnetic force on the rod (Bil) balances the component of weight of the rod<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>m</mi><mi>g</mi><mi>sin</mi><mi>θ</mi><mo>)</mo><mo>,</mo></math> as in figure.</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/fb0451a0-a03a-4b9e-b023-766ce25f29ea-image.png" style="width: 240px; height: 180px;"/></p><p>So, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Bil</mi><mo>=</mo><mi>m</mi><mi>g</mi><mi>sin</mi><mi>θ</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mfenced><mfrac><mi>e</mi><mi>R</mi></mfrac></mfenced><mi>l</mi><mo>=</mo><mi>m</mi><mi>g</mi><mi>sin</mi><mi>θ</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>B</mi><mi>l</mi><mi>e</mi></mrow><mi>R</mi></mfrac><mo>=</mo><mi>m</mi><mi>g</mi><mi>sin</mi><mi>θ</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>B</mi><mi>l</mi><mfenced><mrow><mi>B</mi><mo>/</mo><msub><mi>V</mi><mi>T</mi></msub></mrow></mfenced></mrow><mi>R</mi></mfrac><mo>=</mo><mi>m</mi><mi>g</mi><mi>sin</mi><mi>θ</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mi>T</mi></msub><mo>=</mo><mfrac><mrow><mi>m</mi><mi>g</mi><mi>sin</mi><mi>θ</mi><mi>R</mi></mrow><mrow><msup><mi>B</mi><mn>2</mn></msup><msup><mi>l</mi><mn>2</mn></msup></mrow></mfrac></math></p></div>


slug: a-copper-sphere-cools-from-6-2-c-to-5-0-c-in-10-minutes-and-to-4-2-c-in-the-next-10-minu-32361
tags: ['Physics', 'Thermal Properties of Matter', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch0.db
title:
A copper sphere cools from 6 2 â C to 5 0 â C in 10 minutes and to 4 2 â C in the next 10 minutes. Calculate the temperature of the surroundings.

question:
<div class="question">A copper sphere cools from $62^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$ in 10 minutes and to $42^{\circ} \mathrm{C}$ in the next 10 minutes. Calculate the temperature of the surroundings.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$18.01^{\circ} \mathrm{C}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$26^{\circ} \mathrm{C}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$10.6^{\circ} \mathrm{C}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$20^{\circ} \mathrm{C}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$26^{\circ} \mathrm{C}$</span> </div>

answer:
<div class="solution">By Newton's law of cooling, $\frac{\theta_{1}-\theta_{2}}{t}=-k\left[\frac{\theta_{1}+\theta_{2}}{2}-\theta_{0}\right]$ ....(1)<br/><br/>A sphere cools from $62^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$ in $10 \mathrm{~min}$. $\frac{62-50}{10}=-\mathrm{k}\left[\frac{62+50}{2}-\theta_{0}\right]$ ....(2)<br/>Now, sphere cools from $50^{\circ} \mathrm{C}$ to $42^{\circ} \mathrm{C}$ in next $10 \mathrm{~min} .$<br/>$$<br/>\frac{50-42}{10}=-\mathrm{k}\left[\frac{50+42}{2}-\theta_{0}\right] ....(3)<br/>$$<br/>Dividing eq $^{\text {n }}$. (2) by (3) we get, $\frac{56-\theta_{0}}{46-\theta_{0}}=\frac{1.2}{0.8}$ or $0.4 \theta_{0}=10.4$<br/>Hence $\theta_{0}=26^{\circ} \mathrm{C}$</div>


slug: a-crystal-has-a-coefficient-of-expansion-13-1-0-7-in-one-direction-and-231-1-0-7-in-ev-58466
tags: ['Physics', 'Thermal Properties of Matter', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch0.db
title:
A crystal has a coefficient of expansion 13 Ã 1 0 â 7 in one direction and 231 Ã 1 0 â 7 in every direction at right angles to it. Then the cubical coefficient of expansion is

question:
<div class="question">A crystal has a coefficient of expansion $13 \times 10^{-7}$ in one direction and $231 \times 10^{-7}$ in every direction at right angles to it. Then the cubical coefficient of expansion is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$462 \times 10^{-7}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$244 \times 10^{-7}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$475 \times 10^{-7}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$257 \times 10^{-7}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$475 \times 10^{-7}$</span> </div>

answer:
<div class="solution">$\begin{aligned} \gamma &amp;=\alpha_{1}+\alpha_{2}+\alpha_{3} \\ &amp;=13 \times 10^{-7}+231 \times 10^{-7}+231 \times 10^{-7} \\ &amp;=475 \times 10^{-7} \end{aligned}$</div>


tags: ['Physics', 'Mechanical Properties of Solids', 'BITSAT', 'BITSAT 2013']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0.06</span> </div>
source_db: MarksBatch0.db
title:
A cube is subjected to a uniform volume compression. If the side of the cube decreases by 2% the bulk strain is

slug:
a-cube-is-subjected-to-a-uniform-volume-compression-if-the-side-of-the-cube-decreases-by-2-the-bul-72602

question:
<div class="question">A cube is subjected to a uniform volume compression. If the side of the cube decreases by $2 \%$ the bulk strain is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0.02</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">0.03</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">0.04</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">0.06</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">\(\begin{aligned} \frac{\Delta a}{d} &amp;=2 \% \\ v &amp;=a^{3} \\ \frac{\Delta v}{v} &amp;=3 \frac{\Delta a}{d} \\ &amp;=6 \% \\ &amp;=0.06 \end{aligned}\)</div>


title: A current i flows through a loop as shown in figure. The magnetic field at the Centre O is
slug: a-current-i-flows-through-a-loop-as-shown-in-figure-the-magnetic-field-at-the-centre-o-is-84503
tags: ['Physics', 'Magnetic Effects of Current', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch0.db
question:
<div class="question">A current <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math> flows through a loop as shown in figure. The magnetic field at the Centre <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math> is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/3f5c3755-d32c-404e-96bf-d5888bed3510-aecd7fbf-224b-4799-bc7e-b12a03cde3ac-1.png" style="width: 300px; height: 296px;"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>7</mn><msub><mi>μ</mi><mi>o</mi></msub><mi>i</mi></mrow><mrow><mn>12</mn><mi>r</mi></mrow></mfrac></math> acting downwards</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><msub><mi>μ</mi><mi>o</mi></msub><mi>i</mi></mrow><mrow><mn>12</mn><mi>r</mi></mrow></mfrac></math> acting upwards</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>7</mn><msub><mi>μ</mi><mn>0</mn></msub><mi>i</mi></mrow><mrow><mn>12</mn><mi>r</mi></mrow></mfrac></math> acting upwards</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><msub><mi>μ</mi><mn>0</mn></msub><mi>i</mi></mrow><mrow><mn>12</mn><mi>r</mi></mrow></mfrac></math> acting downwards</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><msub><mi>μ</mi><mn>0</mn></msub><mi>i</mi></mrow><mrow><mn>12</mn><mi>r</mi></mrow></mfrac></math> acting downwards</span> </div>

answer:
<div class="solution"><p>The angle, subtended by arc <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>E</mi></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>π</mi><mn>2</mn></mfrac></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>C</mi></math> at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mo>=</mo><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mn>2</mn></mfrac></math> the effective magnetic field at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math> is</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><msub><mi>B</mi><mrow><mi>D</mi><mi>E</mi></mrow></msub><mo>+</mo><msub><mi>B</mi><mrow><mi>F</mi><mi>C</mi></mrow></msub></math></p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/2bb1ce6b-8698-4747-a5e1-b1c4b7d868a7-1.png" style="width: 280px; height: 275px;"/></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><mi>i</mi></mrow><mrow><mn>4</mn><mi>π</mi><mfenced><mrow><mn>3</mn><mi>r</mi></mrow></mfenced></mrow></mfrac><mo>×</mo><mfrac><mi>π</mi><mn>2</mn></mfrac><mo>+</mo><mfrac><mrow><msub><mi>μ</mi><mn>0</mn></msub><mi>i</mi></mrow><mrow><mn>4</mn><mi>π</mi><mfenced><mi>r</mi></mfenced></mrow></mfrac><mo>×</mo><mfenced><mfrac><mrow><mn>3</mn><mi>π</mi></mrow><mn>2</mn></mfrac></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><msub><mi>μ</mi><mi>o</mi></msub><mi>i</mi></mrow><mrow><mn>8</mn><mi>r</mi></mrow></mfrac><mfenced close="]" open="["><mrow><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>+</mo><mn>3</mn></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>5</mn><msub><mi>μ</mi><mi>o</mi></msub><mi>i</mi></mrow><mrow><mn>12</mn><mi>r</mi></mrow></mfrac></math> acting downwards</p></div>


tags: ['Chemistry', 'Electrochemistry', 'BITSAT', 'BITSAT 2013']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch0.db
title:
A current of 2.0 A passed for 5 hours through a molten metal salt deposits 22.2 g of metal (At wt. = 177 ). The oxidation state of the metal in the metal salt is

slug:
a-current-of-2-0-a-passed-for-5-hours-through-a-molten-metal-salt-deposits-22-2-g-of-metal-at-wt-88128

question:
<div class="question">A current of 2.0 A passed for 5 hours through a molten metal salt deposits $22.2 \mathrm{~g}$ of metal (At wt. $=177$ ). The oxidation state of the metal in the metal salt is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">3</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">4</span> </li> </ul>

answer:
<div class="solution">$\mathrm{m}=\frac{\mathrm{E} \cdot \mathrm{wt} \times \mathrm{Q}}{96500}$
<br/> <br/>$\begin{aligned} \therefore \mathrm{E} . \mathrm{wt} &amp;=\frac{\mathrm{m} \times 96500}{\mathrm{Q}} \\=\frac{22.2 \times 96500}{2 \times 5 \times 60 \times 60}=60.3 \end{aligned}$
<br/> <br/>Oxidation state $=\frac{\text { At wt. }}{\text { Eq. wt. }}=\frac{177}{60.3}=3$</div>


tags: ['Physics', 'Thermodynamics', 'BITSAT', 'BITSAT 2009']
answer: <div class="solution">No Solution available</div>
source_db: MarksBatch0.db
title:
A cyclic process is shown in the p-T diagram. Which of the curves show the same process on a P - V diagram?

slug:
a-cyclic-process-is-shown-in-the-p-t-diagram-which-of-the-curves-show-the-same-process-on-a-p-v-d-89332

question:
<div class="question">A cyclic process is shown in the p-T diagram. Which of the curves show the same process on a $\mathrm{P}$ - $\mathrm{V}$ diagram?<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/o-8UK9Po54w8g9dEv-1EPuWhAq8UOM4iruEEa46yXHY.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/4Yvdldf6HPAimaHiWd2_XC-ufb25mh5CJgIjXJNi6ik.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/1dLNjBpUEZ-s3gQOzMfxU_mUCnVbc5IKgr3Wz65oSrk.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/quZEfbvg6niTaruX23KL8HkrNiMHDASqDRS9pa8ZE-4.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/mh8iXgW4bMwNmhykyKagHV5Ts_TyOvJRul4MbGSMjuA.original.fullsize.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/1dLNjBpUEZ-s3gQOzMfxU_mUCnVbc5IKgr3Wz65oSrk.original.fullsize.png"/></span> </div>


tags: ['Physics', 'Rotational Motion', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch0.db
title:
A cylinder of mass 2 kg is released from rest from the top of an inclined plane of inclination 30 Â° and length 1 m . If the cylinder rolls without slipping, then its speed when it reaches the bottom is [ g = 10 m s - 2 ]

slug:
a-cylinder-of-mass-2-kg-is-released-from-rest-from-the-top-of-an-inclined-plane-of-inclination-30-12196

question:
<div class="question">A cylinder of mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi>kg</mi></math> is released from rest from the top of an inclined plane of inclination <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo>°</mo></math> and length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">m</mi></math>. If the cylinder rolls without slipping, then its speed when it reaches the bottom is [<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mn>10</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></math>]</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>20</mn><mn>3</mn></mfrac><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mn>20</mn><mn>3</mn></mfrac></msqrt><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>10</mn><mn>3</mn></mfrac><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mn>10</mn><mn>3</mn></mfrac></msqrt><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mn>20</mn><mn>3</mn></mfrac></msqrt><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </div>

answer:
<div class="solution"><p>Potential energy of cylinder at top position</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/610ef1cd-4773-43f2-8366-3b0bd8d1f9fa-image.png" style="width: 230px; height: 177px;"/></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>U</mi><mo>=</mo><mi>m</mi><mi>g</mi><mfenced><mrow><mi>A</mi><mi>B</mi></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>2</mn><mo>×</mo><mn>10</mn><mfenced close="]" open="["><mrow><mn>1</mn><mo>.</mo><mi>sin</mi><mn>30</mn><mo>°</mo></mrow></mfenced><mo>  </mo><mfenced close="]" open="["><mtable columnalign="left"><mtr><mtd><mo>∵</mo><mi>sin</mi><mn>30</mn><mo>°</mo><mo>=</mo><mfrac><mrow><mi>A</mi><mi>B</mi></mrow><mrow><mi>B</mi><mi>C</mi></mrow></mfrac></mtd></mtr><mtr><mtd><mo>∴</mo><mi>A</mi><mi>B</mi><mo>=</mo><mn>1</mn><mi>sin</mi><mn>30</mn><mo>°</mo></mtd></mtr></mtable></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>10</mn><mo> </mo><mi mathvariant="normal">J</mi></math></p><p>If <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math> is the linear speed of cylinder when it reaches at bottom, then at bottom, total potential energy of cylinder is converted into kinetic energy,</p><p>i.e. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi><mo>=</mo><mi>U</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>I</mi><msup><mi>ω</mi><mn>2</mn></msup><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup><mo>=</mo><mn>10</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>·</mo><mfrac><mrow><mi>m</mi><msup><mi>r</mi><mn>2</mn></msup></mrow><mn>2</mn></mfrac><mo>·</mo><mfrac><msup><mi>v</mi><mn>2</mn></msup><msup><mi>r</mi><mn>2</mn></msup></mfrac><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup><mo>=</mo><mn>10</mn><mfenced close="]" open="["><mrow><mo>∵</mo><mi>ω</mi><mo>=</mo><mfrac><mi>v</mi><mi>r</mi></mfrac></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo>  </mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mi>m</mi><msup><mi>v</mi><mn>2</mn></msup><mo>=</mo><mn>10</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><msqrt><mfrac><mn>40</mn><mrow><mn>3</mn><mi>m</mi></mrow></mfrac></msqrt><mo>=</mo><msqrt><mfrac><mn>40</mn><mrow><mn>3</mn><mo>×</mo><mn>2</mn></mrow></mfrac></msqrt><mo>=</mo><msqrt><mfrac><mn>20</mn><mn>3</mn></mfrac></msqrt><mo> </mo><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p></div>


